Transformations of Exponential Functions

Transformations of Exponential Functions

Multiple Choice

What is the y-intercept of the function?

• 2

• 3

• 1

• -2

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth

• Exponential Decay

• Linear

• None

Multiple Choice

What is the horizontal asymptote?

• y = 3

• y = -2

• y = -3

• y > -3

Multiple Choice

What is the Domain of this exponential function?

• y=1

• x=0

• All Real Numbers

• x>0

Multiple Choice

What is the horizontal asymptote?

• x = -1

• y = 0

• y > -1

• y = -1

Multiple Choice

Determine the RANGE of the exponential function shown here, defined by the equation $$y=\left(2\right)^x+2$$

• All real numbers

• [2, 3]

• y < 2

• y > 2

Multiple Choice

Is this exponential growth or decay?

• Growth

• Decay

Multiple Choice

Is this exponential growth or decay? Find the growth or decay rate as a PERCENT.

• Growth; Growth of 2%

• Decay; decay of 2%

• Growth; Growth of 20%

• Decay; decay of 7%

Multiple Choice

Which function represents exponential DECAY?

• $$y=a\left(1+r\right)^t$$  

• $$y=r\left(a_n-1\right)^{ }$$  

• $$y=a\left(1+\frac{r}{n}\right)^{nt}$$  

• $$y=a\left(1-r\right)^t$$  

Multiple Choice

Which graph represents an exponential function?

Multiple Choice

What is the horizontal asymptote?

• y = -1

• y = 0

• y < 0

• (1,0)

Multiple Choice

Determine the End behavior of the exponential function as $$x\rightarrow-\infty$$ (left side)

• h(x) → ∞

• h(x) → -∞

•  h(x) →0

• h(x) → 3

Adding or subtracting a 'k' will shift the graph up or down

This also affects the Asymptote and Range

​

​Vertical Shifts

Multiple Choice

If $$y=3^x$$   is translated two units UP, which of the following is the new equation?

• $$y=3^{x-2}+2$$  

• $$y=3^{x-2}$$  

• $$y=3^x+2$$  

• $$y=3^{x+2}$$  

Multiple Choice

If g(x) is a transformation of f(x), describe the transformation. $$f\left(x\right)=2^x$$      $$g\left(x\right)=2^x-4$$   

• Up 4 units

• Down 4 units

• Left 4 units

• Right 4 units

Multiple Choice

What is the range of the exponential function?

$$y=2^x+3$$

• all real numbers

• y > 3

• y < 3

• x > 3

Multiple Choice

What is the Horizontal Asymptote?

• y = -2

• y= 2

• y = 0

• y = 1

Multiple Choice

Which graph best represents

$$y=2^x-4$$  

Adding or subtracting an 'h' in the exponent will shift a graph left or right

​THINK OPPOSITE

Horizontal Shifts

Multiple Choice

What is the transformation?

• Vertical Translation up 1

• Vertical Translation down 1

• Horizontal Translation left 1

• Horizontal Translation right 1

Multiple Choice

The graph

$$g\left(x\right)=2^{\left(x-3\right)}$$ is shown, which statement best describes the transformation from the parent graph  $$f\left(x\right)=2^x$$ .

• Vertically shift up 3

• Vertically shift down 3

• Horizontally shift right 3

• Horizontally shift left 3

Multiple Choice

How has the function $$3^{x+1}-5$$ been transformed from the parent function  $$3^x$$ ?

• Shifted right 1 and up 5

• Shifted left 1 and down 5

• Shifted left 1 and up 5

• Shifted right 1 and down 5

Multiple Choice

 If g(x) is a transformation of f(x), describe the transformation. $$g\left(x\right)=0.5^{x-3}$$    $$f\left(x\right)=0.5^x$$  

• Left 3 units

• Right 3 units

• Up 3 units

• Down 3 units

Multiple Choice

Describe the transformation:

$$f\left(x\right)=4^{x+2}-3$$  

• Translate Up 2 and Right 3

• Translate Right 2 and Down 3

• Translate Left 2 and Down 3

• Translate Down 2 and Right 3

Making the a negative will cause the graph to reflect over the x-axis

​

Reflections

Multiple Choice

What transformation occurs from

$$y=2^x$$  to  $$y=-1\cdot2^x$$  

• Reflection over the x-axis

• Reflection over the y-axis

• Vertically shift down 1 units

• Changes from growth to decay

Multiple Choice

Which equation matches this graph?

Multiple Choice

Which graph shows a reflection of 

$$f\left(x\right)=3^x$$  over the x-axis?

Multiple Choice

What transformations have happened to f(x) = 2^x if the new equation is
 g(x) = -2^(x+3) -6

• It stayed the same

• reflects, up 3, left 6

• reflects, right 3, down 6

• reflects, left 3, down 6

Multiple Choice

What transformations occur in the following function?

• right 3, up 2

• left 3, up 2

• left 3, down 2

• right 3, down 2

a > 1 = Vertical Stretch

(Whole numbers or fractions greater than 1)

0 < a < 1 = Vertical Shrink

(Fractions less than 1)

​Vertical Stretch or Shrink

Multiple Choice

Which of the following is NOT a transformation of the equation

$$f\left(x\right)=3\cdot2^{\left(x-3\right)}+3$$  

• Shift horizontally left 3 units

• Shift vertically up 3 units

• Shift horizontally right 3 units

• Vertically stretched by a factor of 3

Multiple Choice

Is the following equation an exponential growth or decay? Shrink or Stretch?

$$f\left(x\right)=\frac{1}{2}\left(3\right)^x$$  

• Exponential Growth & Vertical Shrink

• Exponential Decay & Vertical Shrink

• Exponential Growth & Vertical Stretch

• Exponential Growth & Vertical Shrink

Multiple Choice

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

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

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

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

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