Common Core: High School - Functions : Graph Exponential, Logarithmic, and Trigonometric Functions: CCSS.Math.Content.HSF-IF.C.7e

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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 #1 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the following function.

Possible Answers:

Screen shot 2016 01 13 at 1.39.13 pm

Screen shot 2016 01 13 at 1.37.23 pm

Screen shot 2016 01 13 at 1.38.39 pm

Screen shot 2016 01 13 at 1.38.57 pm

Screen shot 2016 01 13 at 1.39.34 pm

Correct answer:

Screen shot 2016 01 13 at 1.37.23 pm

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 -intercept.

Recall that  is just a constant,

and any constant raised to zero equals one.

Therefore the -intercept occurs at the point 

Step 2: Graph the function using technology and plot the -intercept. 

Screen shot 2016 01 13 at 1.37.23 pm

 

Example Question #2 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Screen shot 2016 01 13 at 1.39.13 pm

Question3

Screen shot 2016 01 13 at 1.39.34 pm

Screen shot 2016 01 13 at 1.38.57 pm

Question2

Correct answer:

Question3

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 any intercepts.

Recall that the natural log cannot be less than zero and it has a x-intercept of one.

Also recall that the natural log and  cancel each other out which results in,

Since the function is,

a table can be created to find the function values.

Step 2: Graph the function using technology and plot the intercept. 

Question3

Example Question #3 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Question2

Screen shot 2016 01 13 at 1.39.13 pm

Screen shot 2016 01 13 at 1.39.34 pm

Screen shot 2016 01 13 at 1.37.23 pm

Screen shot 2016 01 13 at 1.38.57 pm

Correct answer:

Question2

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 any intercepts.

Recall that the natural log cannot be less than zero and it has a x-intercept of one.

Also recall that the natural log and  cancel each other out which results in,

Step 2: Graph the function using technology and plot the intercept. 

Question2

Example Question #4 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Screen shot 2016 01 13 at 1.39.13 pm

Question4

Question3

Question2

Screen shot 2016 01 13 at 1.39.34 pm

Correct answer:

Question4

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 any intercepts.

Recall that the natural log cannot be less than zero and it has a x-intercept of one.

therefore,

Since the function is,

a table can be created to find the function values.

Step 2: Graph the function using technology and plot the intercept. 

Question4

Example Question #5 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Question5

Screen shot 2016 01 13 at 1.39.34 pm

Question3

Screen shot 2016 01 13 at 1.37.23 pm

Question4

Correct answer:

Question5

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 any intercepts.

Recall that the natural log cannot be less than zero and it has a x-intercept of one.

therefore,

Since the function is,

a table can be created to find the function values.

Step 2: Graph the function using technology and plot the intercept. 

Question5

Example Question #6 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Screen shot 2016 01 13 at 1.37.23 pm

Question3

Question5

Question6

Question4

Correct answer:

Question6

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 any intercepts.

Recall that the natural log cannot be less than zero and it has a x-intercept of one.

therefore,

Since the function is,

a table can be created to find the function values.

Step 2: Graph the function using technology and plot the intercept.

Question6

Example Question #7 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Question5

Screen shot 2016 01 13 at 1.37.23 pm

Question6

Question7

Screen shot 2016 01 13 at 1.39.13 pm

Correct answer:

Question7

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 any intercepts.

Recall that the natural log cannot be less than zero and it has a x-intercept of one.

therefore,

Since the function is,

a table can be created to find the function values.

Step 2: Graph the function using technology and plot the intercept. 

Question7

Example Question #8 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Question8

Question7

Screen shot 2016 01 13 at 1.38.57 pm

Question3

Screen shot 2016 01 13 at 1.38.39 pm

Correct answer:

Question8

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 -intercept.

Recall that  is just a constant,

and any constant raised to zero equals one.

Therefore the -intercept occurs at the point 

Step 2: Graph the function using technology and plot the -intercept. 

Question8

Example Question #9 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Question9

Question7

Question3

Question10

Question6

Correct answer:

Question10

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 -intercept.

Recall that  is just a constant,

and any constant raised to zero equals one.

Since the function is 

Therefore the -intercept occurs at the point 

Step 2: Graph the function using technology and plot the -intercept. 

Question10

Example Question #10 : Graph Exponential, Logarithmic, And Trigonometric Functions: Ccss.Math.Content.Hsf If.C.7e

Graph the function.

Possible Answers:

Question7

Question6

Question9

Question5

Question8

Correct answer:

Question9

Explanation:

This question is testing one's ability to graph exponential functions.

For the purpose of Common Core Standards, "graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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 -intercept.

Recall that  is just a constant,

and any constant raised to zero equals one.

Since the function is 

Therefore the -intercept occurs at the point 

Note that this vertical shift moves the horizontal asymptote up one from zero to one.

Step 2: Graph the function using technology and plot the -intercept. 

Question9

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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
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