Complete the table and graph each exponential function. Then determine the following characteristics for the function $$g\left(x\right)=0.5\left(3\right)^x$$ Growth / Decay

Growth - Increase from left to right

Decay - Decrease from left to right

For the exponential equation $$m\left(x\right)\ =\ 4^x+2$$ , identify the following: Stretch / Shrink by:

No Stretch or Shrink because a = 1

For the exponential equation $$b\left(x\right)=-7\left(\frac{1}{2}\right)^x$$ , identify the following: Shift Left / Right by:

Shift left / right by None because h=0

For the exponential equation $$b\left(x\right)=-7\left(\frac{1}{2}\right)^x$$ , identify the following: Shift Up / Down by:

No Shift Up / Down because k = 0

For the exponential equation $$b\left(x\right)=-7\left(\frac{1}{2}\right)^x$$ , identify the following: Shift Left / Right by:

Shift left / right by None because h=0

For the exponential equation $$y=0.25\left(3\right)^{x+4}-1$$ , identify the following: Growth/Decay because:

Growth of 0.25 because 0.25 > 1

Tyler is given the function: $$y\ =\ \frac{3}{4}\left(5\right)^x+2$$ and needs your help to explain each part. Part A: Tyler says the function is a GROWTH function due to the change factor of 5. Is Tyler correct? Explain your answer in a complete sentence.

Yes, the b value of 5 represents a GROWTH function because 5 > 1

No, the b value of 3/4 represents a DECAY function because 3/4 < 1

Tyler is given the function: $$y\ =\ \frac{3}{4}\left(5\right)^x+2$$ and needs your help to explain each part. Part B: Tyler says the function has a vertical STRETCH by 2. Is Tyler correct? If not stretch, state the correct transformation using a complete sentence.

No, it is a SHRINK by 3/4. The 2 represents the k value, or the asymptote. This means the function shifts UP 2.

Yes, it is a STRETCH by 2. The 2 is the a value and it is greater than 1.

Tyler is given the function: $$y\ =\ \frac{3}{4}\left(5\right)^x+2$$ and needs your help to explain each part. Part C: Tyler thinks the exponential function shifts DOWN by 3/4 units. Is he right? Explain your answer in a complete sentence.

No, it shifts UP by 2 because the K value is 2. The 3/4 is the a value and it means that it shrinks by 3/4.

Yes, is shifts DOWN by 3/4 because the a value is 3/4.

Characteristics of Exponential Functions

Authored by Arrina Brasher

Mathematics

9th Grade

CCSS covered

Used 1+ times

Characteristics of Exponential Functions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Growth - Increases to the Right

Decay - Decreases to the Right

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

y = 1/2

y = 3

1/2

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

(0, 4)

None

(3, 0)

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

(0, 4)

None

(3, 0)

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.HSF-IF.C.7E

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