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Common Core: High School - Functions : High School: 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 #341 : High School: Functions

Solve for using rules of logarithmic functions.

$4e^{x}+5=17$

Possible Answers:

x=3

$x=-\ln3$

x=1

$x=\ln6$

$x=\ln3$

Correct answer:

$x=\ln3$

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.

$4e^{x}+5=17$

Subtract five from both sides and then divide by four.

$\\4e^{x}+5-5=17-5\\4e^{x}=12\\e^x=3$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\\e^x=3 \\ \ln e^x=\ln3 \\x=\ln 3$

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Example Question #6 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

$4e^{x}+5=13$

Possible Answers:

$x=\ln2-1$

$x=\ln1$

$x=\ln2$

x=2

x=e^2

Correct answer:

$x=\ln2$

Explanation:

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

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.

$4e^{x}+5=13$

Subtract five from both sides and then divide by four.

$\\4e^{x}+5-5=13-5\\4e^{x}=8\\e^x=2$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\\e^x=2 \\ \ln e^x=\ln2 \\x=\ln 2$

Report an Error

Example Question #5 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

$4e^{x}-6=12$

Possible Answers:

$x=\ln \frac{9}{2}$

$x=\ln\frac{2}{9}$

$x=-\ln18$

$x=\ln2+18$

$x=\ln18-2$

Correct answer:

$x=\ln \frac{9}{2}$

Explanation:

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

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.

$4e^{x}-6=12$

Add six from both sides and then divide by four.

$\\4e^{x}-6+6=12+6\\4e^{x}=18\\\\e^x=\frac{9}{2}$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\\e^x=\frac{9}{2} \\\\ \ln e^x=\ln\frac{9}{2} \\x=\ln \frac{9}{2}$

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Example Question #342 : High School: Functions

Solve for using rules of logarithmic functions.

$e^{x-4}-2=10$

Possible Answers:

$x=\ln12+4$

$x=\ln12-4$

$x=\ln4$

$x=\ln6+2$

$x=\ln6-2$

Correct answer:

$x=\ln12+4$

Explanation:

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

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.

$e^{x-4}-2=10$

Add two from both sides.

$\\e^{x-4}-2+2=10+2 \\e^{x-4}=12$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\\e^{x-4}=12 \\ \ln e^{x-4}=\ln 12\\ x-4=\ln 12\\x=\ln 12+4$

Report an Error

Example Question #2 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

$e^{x-4}-1=5$

Possible Answers:

$x=\ln 6-4$

$x=\ln 6$

$x=\ln 6+4$

$x=\ln 6-2$

$x=\ln 6+2$

Correct answer:

$x=\ln 6+4$

Explanation:

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

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.

$e^{x-4}-1=5$

Add one from both sides.

$\\e^{x-4}-1+1=5+1 \\e^{x-4}=6$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\\e^{x-4}=6 \\ \ln e^{x-4}=\ln 6\\ x-4=\ln 6\\x=\ln 6+4$

Report an Error

Example Question #10 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Solve for using rules of logarithmic functions.

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

Possible Answers:

$x=\ln 2-4$

$x=\ln 2+2$

$x=\ln 2+4$

$x=\ln 2-2$

$x=\ln 2+1$

Correct answer:

$x=\ln 2+4$

Explanation:

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

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.

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

Add one from both sides.

$\\e^{x-4}-1+1=1+1 \\e^{x-4}=2$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\\e^{x-4}=2 \\ \ln e^{x-4}=\ln 2\\ x-4=\ln 2\\x=\ln 2+4$

Report an Error

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:

$x=\ln1$

x=3

x=4

$x=\ln2$

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.

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 .

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

Report an Error

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:

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

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

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

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

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

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) .

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

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Example Question #1 : 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:

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

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

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

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

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

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 #2 : 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

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All Common Core: High School - Functions Resources

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Common Core: High School - Functions : High School: Functions

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

All Common Core: High School - Functions Resources

Example Questions

Example Question #341 : High School: Functions

Example Question #6 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Example Question #5 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Example Question #342 : High School: Functions

Example Question #2 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

Example Question #10 : Express Exponential Models As Logarithmic Solutions: Ccss.Math.Content.Hsf Le.A.4

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

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

All Common Core: High School - Functions Resources

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