Common Core: High School - Functions : Building Functions

Study concepts, example questions & explanations for Common Core: High School - Functions

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All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Jane wants to buy a new backpack for next year. The backpack that she has her eye on costs  Jane works as a car washer and gets paid  an hour. If Jane works  hours every week, how many weeks of work will it take for her to earn enough money to buy the new backpack?

Possible Answers:

Jane will need to work for six weeks.

Jane will need to work for three weeks.

Jane will need to work for two weeks.

Jane will need to work for five weeks.

Jane will need to work for four weeks.

Correct answer:

Jane will need to work for three weeks.

Explanation:

This question is testing one's ability to recognize functions in everyday situations and build the mathematical model that shows the relationship between two quantities. A question such as this requires examination into the behavior between the quantities, whether it be explicit expression, a recursive process, or a multi-step calculation. It also requires the use of algebraic operations to solve the question at hand and then build a function that models the relationship.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Jane need to work to earn enough money to buy the new backpack?

Step 2: Identify what is given/known from the question.

The backpack costs 

Jane earns 

Jane works 

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

Using algebraic operations divide by  on both sides to calculate the number of weeks Jane will need to work.

Example Question #11 : Functions Describing A Relationship Between Two Quantities: Ccss.Math.Content.Hsf Bf.A.1

Jenny wants to buy a new bike for next year. The bike that she has her eye on costs . Jenny works mowing lawns and gets paid  per lawn. How many lawns will Jenny need to mow to earn enough money to buy a new bike.

Possible Answers:

Jenny will need to mow  lawns.

Jenny will need to mow  lawns.

Jenny will need to mow  lawns.

Jenny will need to mow  lawns.

Jenny will need to mow  lawns.

Correct answer:

Jenny will need to mow  lawns.

Explanation:

This question is testing one's ability to recognize functions in everyday situations and build the mathematical model that shows the relationship between two quantities. A question such as this requires examination into the behavior between the quantities, whether it be explicit expression, a recursive process, or a multi-step calculation. It also requires the use of algebraic operations to solve the question at hand and then build a function that models the relationship.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many lawns will Jenny need to work to earn enough money to buy the new bike?

Step 2: Identify what is given/known from the question.

The bike costs 

Jenny earns 

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

Using algebraic operations divide by  on both sides to calculate the number of lawns Jenny will need to work.

Example Question #1 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every two days and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had three blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Possible Answers:

Correct answer:

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is three.

The fertilizer produces four blooms every two days. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

Example Question #2 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every two days and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had one bloom. Write a function that models the number of blooms in  days since the fertilizer was added.

Possible Answers:

Correct answer:

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is one.

The fertilizer produces four blooms every two days. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

Example Question #3 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had three blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Possible Answers:

Correct answer:

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is three.

The fertilizer doubles the blooms every day. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is two every day. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

Example Question #4 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had two blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Possible Answers:

Correct answer:

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is two.

The fertilizer doubles the blooms every day. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is two every day. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

Example Question #5 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had five blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Possible Answers:

Correct answer:

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is five.

The fertilizer doubles the blooms every day. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is two every day. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

Example Question #6 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms triple every day and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had two blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Possible Answers:

Correct answer:

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is two.

The fertilizer triples the blooms every day. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is three every day. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

Example Question #7 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms triple every day and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had four blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Possible Answers:

Correct answer:

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is four.

The fertilizer triples the blooms every day. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is three every day. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

Example Question #8 : Combining Standard Function Types By Arithmetic Operations: Ccss.Math.Content.Hsf Bf.A.1b

Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms triple every two days and can be modeled by a function  which depends on  days. Before the fertilizer is added to the pot, Janet had four blooms. Write a function that models the number of blooms in  days since the fertilizer was added.

Possible Answers:

Correct answer:

Explanation:

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is four.

The fertilizer triples the blooms every two days. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is three every two days. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept
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