Exponential Functions Part A 2021 Lesson/Practice

Graphs of Exponential Functions Lesson/Practice

Multiple Choice

The relationship is __________because each y-value is _____________the value before it.

• linear, 3 times

• linear, 4 more than

• exponential, 3 times

• exponential, 4 more than

Multiple Choice

Is the relationship linear, exponential, or neither?

• Linear with a constant rate of change of 3/5

• Linear with a constant rate of change of 3/1

• Exponential with a constant factor of 3/1

• Exponential with constant factor of 3/5

• Neither

Multiple Select

Which of the following are examples of exponential growth? (Choose all that apply)

• $y\ =\ 5\left(\frac{1}{2}\right)^x$

• $y\ =\ 5\left(\frac{3}{2}\right)^x$

• $y\ =\ 0.2\left(3\right)^x$
  

• $y\ =\ 600\left(0.98\right)^x$
  

Multiple Choice

Which could represent the graph of the function

 $g\left(x\right)=6\left(\frac{8}{3}\right)^x$  ?

Multiple Choice

Which graph matches this equation?

Multiple Choice

Which equation matches this graph?

Multiple Choice

Which graph matches the equation?

Multiple Choice

Which graph matches the equation?

•  $y=-3\left(4\right)^x+2$ 

•  $y=-3\left(\frac{1}{4}\right)^x+2$ 

•  $y=3\left(4\right)^x+2$ 

•  $y=3\left(\frac{1}{4}\right)^x+2$ 

Multiple Choice

Which graph matches the equation?

•  $y=-3\left(3\right)^x+2$ 

•  $y=-3\left(\frac{1}{3}\right)^x+2$ 

•  $y=-3\left(3\right)^x-2$ 

•  $y=-3\left(\frac{1}{3}\right)^x-2$ 

Multiple Choice

What is the equation for this graph?

• $y=2^x-4$

• $y=2^x-5$
  

• $y=3^x-4$
  

• $y=3^x-5$
  

Multiple Choice

The parent function  $f\left(x\right)=3^x$  has been shifted to the left 2 units, reflected vertically over the x-axis, and shifted up 5 units. What equation models the transformed graph? 

•  $f\left(x\right)=-3^{x-2}+5$  

•  $f\left(x\right)=3^{x-2}-5$  

•  $f\left(x\right)=-3^{x+2}+5$  

•  $f\left(x\right)=3^{x+2}-5$  

Multiple Choice

Consider the parent function f(x) = 4^x. Which statement describes the graph g(x) = f(x - 3) + 5.

• The graph would be translated right 3 and down 5.

• The graph would be translated left 3 and down 2.

• The graph would be translated right 3 and up 5.

• The graph would be translated left 3 and up 5.

Multiple Choice

Which of the following describes the transformation of  $g\left(x\right)=\frac{1}{2}\cdot2^{\left(x+2\right)}-3$  from the parent graph  $f\left(x\right)=2^x$  

• Vertically shift down 3, horizontally shift left 2, and vertically stretch by 1/2 units

• Vertically shift up 3, horizontally shift left 2, and vertically compressed 1/2 units

• Vertically shift down 3, horizontally shift left 2, and vertically compressed 1/2 units

• Vertically shift up 3, horizontally shift right2, and vertically compressed 1/2 units

Multiple Choice

What are the transformations of the function

 $g\left(x\right)=-3\left(4\right)^{x-2}-5$  from the parent function?

• reflect, stretch

  right 2, down 5

• stretch

  right 2

  down 5

• reflect, shrink

  left 2, down 5

• shrink

  left 2

  down 5

 Characteristics of Exponentials

• Domain: all real numbers

• Range: y > - 3

• y-intercept (0,-2)

• End Behavior: as $x\ \rightarrow\ \infty\ then\ f\left(x\right)\ \rightarrow\ \infty$  

   $x\ \rightarrow\ -\infty\ then\ f\left(x\right)\ \rightarrow\ -3$  

Multiple Choice

What is the equation of the horizontal asymptote for the equation  $y=2\left(3\right)^x-4$  ?

•  $y=-4$  

•  $y=-2$  
  

•  $y=2$  
  

•  $y=3$  
  

Multiple Choice

What is the y-intercept of the graph represented by the equation  $y=5\left(4\right)^x-3$  ?

•  $\left(0,-3\right)$  

•  $\left(0,1\right)$  
  

•  $\left(0,\ 2\right)$  
  

•  $\left(0,17\right)$  
  

Multiple Choice

What is the domain of the graph?

• $(-∞,∞)$
  

• $(-2,∞)$
  

• $(-4,4)$
  

• $(-∞,2)$
  

Multiple Choice

What is the range of this graph?

• $y>-3$

• $(0,-3)$
  

• $y>-6$
  

• $y<-6$
  

Multiple Choice

End Behavior:   As  $x→∞,\ f(x)→$  

•  $-4$  
  

•  $-3$  
  

•  $∞$  
  

•  $-∞$  
  

Multiple Choice

End Behavior:   As  $x→-∞,\ f(x)→$  

•  $-4$  
  

•  $-3$  
  

•  $∞$  
  

•  $-∞$  
  

Multiple Choice

What is the Range of the function graphed?

• $(-8,∞)$

• $[-8,∞)$
  

• $(-∞,∞)$
  

• $(∞,-8)$
  

Multiple Choice

Which equation matches the graph?

• y = 4^{x + 3}

• y = 4^{x - 3}

• y = 4^x + 3

• y = 4^x - 3