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

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 #131 : High School: Functions

Graph the function.

f(x)=e^x+2

Possible Answers:

Question9

Question10

Question11

Question6

Screen shot 2016 01 13 at 1.37.23 pm

Correct answer:

Question11

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,

$e\approx2.718$

and any constant raised to zero equals one.

$\\f(x)=e^{x} \\f(0)=e^0\\f(0)=1$

Since the function is

f(x)=e^x+2

f(0)=e^0+2=1+2=3

Therefore the -intercept occurs at the point (0,3)

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

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

$\begin{tabular}{ c c } x & y \\ \hline -1& 2.369 \\ 0& 3\\ 1&4.718 \end{tabular}$

Question11

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Example Question #132 : High School: Functions

Graph the function.

f(x)=e^x-1

Possible Answers:

Question10

Question11

Question9

Question3

Question12

Correct answer:

Question12

Explanation:

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

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,

$e\approx2.718$

and any constant raised to zero equals one.

$\\f(x)=e^{x} \ \\f(0)=e^0\\f(0)=1$

Since the function is

f(x)=e^x-1

f(0)=e^0-1=1-1=0

Therefore the -intercept occurs at the point (0,0)

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.

$\begin{tabular}{ c c } x & y \\ \hline -1& -0.632 \\ 0& 0\\ 2&6.389 \end{tabular}$

Question12

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

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

All Common Core: High School - Functions Resources

Example Questions

Example Question #131 : High School: Functions

Example Question #132 : High School: Functions

All Common Core: High School - Functions Resources

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