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Common Core: High School - Functions : Linear, Quadratic, & Exponential Models*

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

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Example Question #11 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

$e^{x-4}-1=0$

Possible Answers:

x=4

$x=\ln2$

$x=\ln1$

x=3

x=2

Correct answer:

x=4

Explanation:

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and dare numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

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: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$e^{x-4}-1=0$

Add one from both sides.

$\\e^{x-4}-1+1=0+1 \\e^{x-4}=1$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$ and $\ln1=0$

Step 3: Apply logarithmic rules to solve for .

$\\e^{x-4}=1 \\ \ln e^{x-4}=\ln 1\\ x-4=\ln 1\\x=\ln 1+4\\x=0+4\\x=4$

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Example Question #1 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$500$ to produce a certain play. If the play sells tickets for $\$10$ each what is the function P(t)

that represents the net profit of the play?

Possible Answers:

$P(t)=-\$10t+\$500$

$P(t)=\$10t-\$500$

$P(t)=-\$10t-\$500$

$P(t)=\$10-\$500t$

$P(t)=\$10t+\$500$

Correct answer:

$P(t)=\$10t-\$500$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

For the purpose of Common Core Standards, interpret parameters in a linear or exponential function in terms of a context, falls within the Cluster B of interpret expressions for functions in terms of the situation they model concept (CCSS.Math.content.HSF.LE.B).

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$10 \\ \textup{Production Costs}=\$500 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$10t-\$500$

Report an Error

Example Question #2 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$550$ to produce a certain play. If the play sells tickets for $\$8$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$8t-\$550$

$P(t)=\$550t-\$8$

$P(t)=\$8t-\$500$

$P(t)=\$500t-\$8$

$P(t)=\$10t-\$550$

Correct answer:

$P(t)=\$8t-\$550$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$8 \\ \textup{Production Costs}=\$550 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$8t-\$550$

Report an Error

Example Question #3 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's art department spends $\$100$ on art supplies. If the department sells each art piece for $\$2$ each what is the function A(t) that represents the net profit of the art department?

Possible Answers:

$A(t)=\$2t+\$10$

$A(t)=\$2t-\$10$

$A(t)=\$2t-\$100$

$A(t)=\$2t+\$100$

$A(t)=\$1t-\$100$

Correct answer:

$A(t)=\$2t-\$100$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs}$

Recall that the art sales profit is the product of the price of the art piece and the number of pieces sold.

Step 2: Identify the known values.

$\\ \textup{Cost of an art piece}=\$2 \\ \textup{Art Supply Costs}=\$100 \\ t=\textup{number of art pieces sold} \\A(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create A(t) .

$\\ \textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs} \\A(t)=\$2t-\$100$

Report an Error

Example Question #4 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's art department spends $\$325$ on art supplies. If the department sells each art piece for $\$10$ each what is the function A(t) that represents the net profit of the art department?

Possible Answers:

$A(t)=\$10t-\$325$

$A(t)=\$325t+\$10$

$A(t)=\$10t-\$350$

$A(t)=\$325t-\$10$

$A(t)=\$10t+\$325$

Correct answer:

$A(t)=\$10t-\$325$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs}$

Recall that the art sales profit is the product of the price of the art piece and the number of pieces sold.

Step 2: Identify the known values.

$\\ \textup{Cost of an art piece}=\$10 \\ \textup{Art Supply Costs}=\$325 \\ t=\textup{number of art pieces sold} \\A(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create A(t) .

$\\ \textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs} \\A(t)=\$10t-\$325$

Report an Error

Example Question #5 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$160$ to produce a certain play. If the play sells tickets for $\$4$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$4t-\$160$

$P(t)=\$4t+\$160$

$P(t)=\$4-\$160$

$P(t)=\$160t+\$4$

$P(t)=\$160t-\$4$

Correct answer:

$P(t)=\$4t-\$160$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$4 \\ \textup{Production Costs}=\$160 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$4t-\$160$

Report an Error

Example Question #6 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$240$ to produce a certain play. If the play sells tickets for $\$12$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$12t-\$240$

$P(t)=\$240t+\$12$

$P(t)=\$240t-\$12$

$P(t)=\$240-\$12$

$P(t)=\$12t+\$240$

Correct answer:

$P(t)=\$12t-\$240$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$12 \\ \textup{Production Costs}=\$240 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$12t-\$240$

Report an Error

Example Question #7 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's art department spends $\$300$ on art supplies. If the department sells each art piece for $\$5$ each what is the function A(t) that represents the net profit of the art department?

Possible Answers:

$A(t)=\$300-\$5$

$A(t)=\$5t-\$300$

$A(t)=\$5t+\$300$

$A(t)=\$300t-\$5$

$A(t)=\$300t+\$5$

Correct answer:

$A(t)=\$5t-\$300$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs}$

Recall that the art sales profit is the product of the price of the art piece and the number of pieces sold.

Step 2: Identify the known values.

$\\ \textup{Cost of an art piece}=\$5 \\ \textup{Art Supply Costs}=\$300 \\ t=\textup{number of art pieces sold} \\A(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create A(t) .

$\\ \textup{Net Profit}=\textup{Art Sales Profit}-\textup{Art Supply Costs} \\A(t)=\$5t-\$300$

Report an Error

Example Question #8 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$750$ to produce a certain play. If the play sells tickets for $\$15$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$750t-\$15$

$P(t)=\$15t-\$750$

$P(t)=\$750-\$15$

$P(t)=\$750t+\$15$

$P(t)=\$15t+\$750$

Correct answer:

$P(t)=\$15t-\$750$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$15 \\ \textup{Production Costs}=\$750 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$15t-\$750$

Report an Error

Example Question #9 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

A school's theater department spends $\$190$ to produce a certain play. If the play sells tickets for $\$8.50$ each what is the function P(t) that represents the net profit of the play?

Possible Answers:

$P(t)=\$8.50t-\$190$

$P(t)=\$8.50t+\$190$

$P(t)=\$8.50-\$190t$

$P(t)=\$8.50+\$190t$

$P(t)=\$8.50-\$190$

Correct answer:

$P(t)=\$8.50t-\$190$

Explanation:

This question tests one's ability to recognize parameters of a function and one's understanding of dealing with said parameters in the context of a problem.

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 the general function that describes the situation.

$\textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs}$

Recall that the ticket sales profit is the product of the price of the ticket and the number of tickets sold.

Step 2: Identify the known values.

$\\ \textup{Cost of Ticket}=\$8.50 \\ \textup{Production Costs}=\$190 \\ t=\textup{number of tickets sold} \\P(t)=\textup{Net Profit}$

Step 3: Substitute known values into general function to create P(t) .

$\\ \textup{Net Profit}=\textup{Ticket Sales Profit}-\textup{Production Costs} \\P(t)=\$8.50t-\$190$

Report an Error

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All Common Core: High School - Functions Resources

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Common Core: High School - Functions : Linear, Quadratic, & Exponential Models*

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

All Common Core: High School - Functions Resources

Example Questions

Example Question #11 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Example Question #1 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #2 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #3 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #4 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #5 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #6 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #7 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #8 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

Example Question #9 : Interpret Function Parameters: Ccss.Math.Content.Hsf Le.B.5

All Common Core: High School - Functions Resources

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