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Common Core: High School - Functions : Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

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Example Questions

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Example Question #11 : Graph's Domain: Ccss.Math.Content.Hsf If.B.5

Q11

A vehicle starts to increase its speed after 100 minutes at a rate of miles per hour every five minutes for 200 minutes resulting in a maximum speed near 80 miles per hour. If f(x) represents this function, what is the domain of ?

Possible Answers:

$\textup{Domain: }[20,40]$

$\textup{Domain: }[100,200]$

$\textup{Domain: }[0,40]$

$\textup{Domain: }[20,50]$

$\textup{Domain: }[2,40]$

Correct answer:

$\textup{Domain: }[20,40]$

Explanation:

This particular question is testings one's ability to recognize characteristics of a function in terms of its context. Specifically, it is testing the ability to identify the domain of a function, or in other words, the possible input values that logically and mathematically work for the situation that is described by f(x)

For the purpose of Common Core Standards, "relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes" falls within the Cluster B of "interpret functions that arise in applications in terms of the context" concept (CCSS.MATH.CONTENT.HSF-IF.B.5).

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.

This question is asking to find the domain, possible x values that make sense for this situation

Step 2: Use the information that describes f(x)

and create a graph that could possibly fit.

Let us identify the known information of the function.

is in intervals of "miles per every five minutes" and goes from zero to 200 minutes. Therefore to find the units that the

-axis will have, convert 200 minutes into intervals of five minutes.

$200\text{ minutes}\times\frac{1 \text{interval}}{5\text{minutes}}=40\text{ intervals}$

Since the question states, "A vehicle starts to increase its speed after 100 minutes at a rate of

miles per hour every five minutes for 200 minutes", a linear relationship being time and speed is assumed.

Using the known information creates the graph below.

Q11

Step 3: Using the graph above, identify the domain.

Recalling that the domain of a function is the interval of

values that result in a real output that lies in the range of the function. In mathematical terms,

$\textup{Domain: }[20,40]$ .

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Example Question #12 : Graph's Domain: Ccss.Math.Content.Hsf If.B.5

Q12

A vehicle decrease its speed after 75 minutes at a rate of miles per hour every five minutes for 225 minutes resulting in a minimum speed of 10 miles per hour. If f(x) represents this function, what is the domain of ?

Possible Answers:

$\textup{Domain: }[15,55]$

$\textup{Domain: }[75,175]$

$\textup{Domain: }[15,45]$

$\textup{Domain: }[75,225]$

$\textup{Domain: }[15,75]$

Correct answer:

$\textup{Domain: }[15,45]$

Explanation:

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.

This question is asking to find the domain, possible x values that make sense for this situation

Step 2: Use the information that describes f(x)

and create a graph that could possibly fit.

Let us identify the known information of the function.

is in intervals of "miles per every five minutes" and goes from zero to 225 minutes. Therefore to find the units that the

-axis will have, convert 225 minutes into intervals of five minutes.

$225\text{ minutes}\times\frac{1 \text{interval}}{5\text{minutes}}=45\text{ intervals}$

Since the question states, "A vehicle decrease its speed after 75 minutes at a rate of

miles per hour every five minutes for 225 minutes", a linear relationship being time and speed is assumed.

Using the known information creates the graph below.

Q12

Step 3: Using the graph above, identify the domain.

Recalling that the domain of a function is the interval of

values that result in a real output that lies in the range of the function. In mathematical terms,

$\textup{Domain: }[15,45]$ .

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Common Core: High School - Functions : Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

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

All Common Core: High School - Functions Resources

Example Questions

Example Question #11 : Graph's Domain: Ccss.Math.Content.Hsf If.B.5

Example Question #12 : Graph's Domain: Ccss.Math.Content.Hsf If.B.5

All Common Core: High School - Functions Resources

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