Exponential Functions

Exponential Functions

Exponential functions have a variable as an exponent

Multiple Choice

Which of the following is an exponential function?

• $$f\left(x\right)=x^2$$

• $$f\left(x\right)=3x^3$$

• $$y=x^3$$

• $$f\left(x\right)=3^x$$

Exponential Functions

Multiple Choice

What is the initial value in

$$y=4\left(2\right)^x$$  

• 4

• 2

• x

Multiple Choice

What is the y-intercept of

$$y=-2\left(7\right)^x$$  

• (-2, 0)

• (0, 7)

• x

• (0, -2)

• (4, 2)

Multiple Choice

What is the starting amount in the problem

$$f\left(x\right)=300\left(1.05\right)^x$$  

• 300

• 1.05

• x

• y

Multiple Choice

What is the growth or decay factor for the equation

$$f\left(x\right)\ =\ 25\left(4\right)^x$$  

• 25

• 4

Exponential Growth vs Decay

Multiple Choice

What is

$$b^0$$  

• -1

• 0

• 1

Multiple Select

Select the functions that are exponential growth.

• $$y=-2\left(3\right)^x$$

• $$f\left(x\right)=3\left(1.09\right)^x$$

• $$f\left(x\right)=4\left(\frac{1}{3}\right)^x$$

• $$y=0.5\left(\frac{3}{2}\right)^x$$

The Basics REVIEW

More Basics

Multiple Choice

Write the equation of the exponential function for the given table.

hint: Find the initial value (a) and common ratio (b) and put into $$y=a\left(b\right)^x$$

• $$y=3^x$$

• $$y=12\left(3\right)^x$$

• $$y=3\left(4\right)^x$$

• $$y=4\left(3\right)^x$$

Multiple Choice

Write the equation of the exponential function for the given table.

hint Find the initial value (a) and common ratio (b) and put into $$y=a\left(b\right)^x$$

• $$y=-2\left(\frac{1}{2}\right)^x$$

• $$y=2\left(\frac{1}{2}\right)^x$$

• $$y=2\left(2\right)^x$$

• $$y=\frac{1}{2}\left(2\right)^x$$

Multiple Choice

Write the equation of the exponential function for the given table.

hint: Find the initial value (a) and common ratio (b) and put into $$y=a\left(b\right)^x$$

• $$y=2\left(\frac{1}{3}\right)^x$$

• $$y=-2\left(\frac{1}{3}\right)^x$$

• $$y=\frac{1}{3}\left(2\right)^x$$

• $$y=2\left(-\frac{1}{3}\right)^x$$

Multiple Choice

Which function represents the table of values?

hint: Find the initial value (a) and common ratio (b) and put into $$y=a\left(b\right)^x$$

• f(x) = 4x

• f(x) = x⁴

• f(x) = 4^x

• f(x) = 4^x-1

Multiple Choice

What exponential function models the graph?

• $$y=2\left(1\right)^x$$

• $$y=1\left(\frac{1}{2}\right)^x$$

• $$y=1\left(2\right)^x$$

• $$y=1\left(x\right)^2$$

• k moves entire graph up or down.

• f(x) = 2^x

  Parent Function (Orange Graph)

• g(x) = 2^x + 3 (blue graph)

• h(x) = 2^x - 3 (red graph)

Parent Function and Vertical Shifts

cont.

Multiple Choice

How has the function $$y=2^x+3$$ been transformed from the parent function  $$y=2^x$$ ?

• Shifted up 3

• Shifted down 3

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

How has the function $$y=7\left(3\right)^x-5$$ been transformed from the parent function  $$y=7\left(3\right)^x$$ ?

• Shifted up 5

• Shifted down 5

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

How has the function $$y=4\left(3\right)^x-2$$ been transformed from the parent function  $$y=4\left(3\right)^x$$ ?

• Shifted up 2

• Shifted down 2

• Reflection over the x-axis

• Reflection over the y-axis

Horizontal Transformations

y=a(b)^(x-h) 

• h moves entire graph left or right.

• f(x) = 2^x

  Parent Function (Orange Graph)

• g(x) = 2^x+3 (blue graph)

• h(x) = 2^x-3 (red graph)

Parent Function and horizontal Shifts

cont.

Multiple Choice

The parent function  $$f\left(x\right)=3^x$$   is shown in red and is translated. What is the equation of the green graph?

• $$g\left(x\right)=3^x+2$$  

• $$g\left(x\right)=3^x-2$$  

• $$g\left(x\right)=3^{x-2}$$  

• $$g\left(x\right)=3^{x+2}$$  

Multiple Choice

The parent function  $$f\left(x\right)=2^x$$   is shown in red and is translated. What is the equation of the green graph?

• $$g\left(x\right)=2^x+3$$  

• $$g\left(x\right)=2^x-3$$  

• $$g\left(x\right)=2^{\left(x+3\right)}$$  

• $$g\left(x\right)=2^{\left(x-3\right)}$$  

Multiple Choice

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

• Vertically stretched by a factor of 2, right 3, and up 1

• Vertically compressed by a factor of 1/2, left 3 and down 1

• Vertically compressed by a factor of 1/2, right 3, and down 1

• Vertically stretched by a factor of 2, left 3, and up 1

​Exponential Functions Review