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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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Flashcards: Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

Which value for proves that the function f(x)=e^x will increases faster than the function g(x)=3x+1 ?

$x\geq1$

$x\leq1$

$x\geq2$

$x\geq3$

$x\leq2$

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Flashcards: Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

Which value for proves that the function f(x)=e^x will increases faster than the function g(x)=3x+1 ?

Your answer:

$x\geq1$

Your answer:

$x\leq1$

Your answer:

$x\geq3$

Your answer:

$x\leq2$

Correct answer:

$x\geq2$

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

For the purpose of Common Core Standards, "Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function" falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.3).

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 technology to graph f(x) .

Screen shot 2016 01 14 at 7.53.13 am

Step 2: Use technology to graph g(x) .

Screen shot 2016 01 14 at 7.54.37 am

Step 3: Compare the graphs of f(x) and g(x) .

Screen shot 2016 01 14 at 7.54.10 am

Graphically, it appears that x=2 is the point where g(x) increases more rapidly than f(x) . Substitute two into both functions to algebraic verify the assumption.

f(2)=e^2=(2.718)^2=7.389

g(2)=3(2)+1=7

Since

$7.389>7\Rightarrow f(2)>g(2)\Rightarrow x>2$

Step 4: Answer the question.

For values $x\geq2$ , $f(x)\geq g(x)$ .

Flashcards: Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

Which value for proves that the function f(x)=e^x will increases faster than the function g(x)=x ?

$x\geq1$

$\text{ For all values of }x\text{, } f(x)=e^x \text{ is larger than } y=x.$

$x\geq0$

$x\geq2$

$x\geq8$

Report an Error Copyright Notice

Flashcards: Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

Which value for proves that the function f(x)=e^x will increases faster than the function g(x)=x ?

Your answer:

$x\geq1$

Your answer:

$x\geq0$

Your answer:

$x\geq2$

Your answer:

$x\geq8$

Correct answer:

$\text{ For all values of }x\text{, } f(x)=e^x \text{ is larger than } y=x.$

Explanation:

This question is testing one's ability to identify the end behavior of two functions as they relate to one another by constructing graphs.

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 technology to graph f(x) .

Step 2: Use technology to graph g(x) .

Q2 2

Step 3: Compare the graphs of f(x) and g(x) .

Q2 3

Graphically, it appears that f(x) is larger than g(x) for all values of .

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All Common Core: High School - Functions Resources

Flashcards: Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

Flashcards: Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

Flashcards: Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

Flashcards: Exponential Functions Exceeding Polynomial Functions: CCSS.Math.Content.HSF-LE.A.3

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