Transformations of Exponential & Logarithmic Functions

Unit 9: Exponential & Logarithmic Functions

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Multiple Choice

if $$y=2^x$$   what is y when x = 0, 2, 4?

• 1, 2 and 8

• 1, 4 and 16

• 0, 4 and 8

• 1, 2 and 8

Exponential Functions Intro

• Exponential Functions have the variable as an exponent

• The base can be any positive number

• The domain of exponential functions is always all real numbers

• the range for the parent is (0,∞)

• The parent function has a horizontal asymptote at y=0.

• The y-intercept is at (0,1)

Exponential Functions have a variable in the exponent

Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• $$y=\left(-2\right)^x$$  

• f(x) = 3^x

Vertical Transformations & Asymptote/Range

• If your graph is translated vertically, your asymptote and range will be affected

• Remember that the range for the parent function is (0,∞)

• The asymptote for the parent function is y=0

Multiple Choice

Identify the asymptote of the function $$-3\left(3\right)^x+4$$  

• y = -3

• y = 1

• y = 4

Multiple Choice

Determine the range for the function

f(x) = 3(2)^x-4 + 5

• [5,∞)

• (5,∞)

• [4,∞)

• (4,∞)

Multiple Choice

What is the range of this function?

• (-∞,0)

• (0,∞)

• (-∞,4)

• (4,∞)

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

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

• Shifted up 5

• Shifted down 5

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

What is the domain of the function shown below?

• (-2,5)

• (0,12)

• $$\left(0,\infty\right)$$  

• All Real Numbers

Multiple Choice

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

• Shifted up 5

• Shifted down 5

• Reflection over the x-axis

• Reflection over the y-axis

Multiple Choice

• $$-3\left(3\right)^x+2$$

• $$-3\left(\frac{1}{3}\right)^x+2$$

• $$-3\left(3\right)^x-2$$

• $$-3\left(\frac{1}{3}\right)^x-2$$

Multiple Choice

Using the parent function  $$y=\log_3x$$   what would the graph of  $$y=\log_3\left(x+5\right)$$   look like?

• Horizontal shift left 5 units

• Horizontal shift right 5 units

• Vertical shift up 5 units

• Vertical shift down 5 units

Multiple Choice

Where is the asymptote?

• x = 1

• y = 1

• x = -1

• y = -1

Multiple Choice

Find the corresponding graph of
$$\log_3\left(x-1\right)+4$$  

Multiple Choice

What is the change in the graphs from f(x) to g(x)?

$$f\left(x\right)=\log_8x$$ to  $$g\left(x\right)=\log_8\left(x+9\right)-7\$$  

• Right nine and down seven

• Left nine and down seven

• Left nine and up seven

• Right nine and up seven

Multiple Choice

What is the range of $$y=\log_3\left(x-3\right)-2$$  

• $$\left(-\infty,\infty\right)$$  

• $$\left(2,\infty\right)$$  

• $$\left(-2,\infty\right)$$  

• $$\left(-\infty,2\right)$$  

Explanation Slide...

The domain represents all possible input values for a function. In this case, the domain is (1, ∞) because the function is defined for all real numbers greater than 1.

Multiple Choice

What is the domain?

• (-∞, ∞)

• (0, ∞)

• [1, ∞)

• (1, ∞)

Multiple Choice

What is the Vertical Asymptote for the graph  $$y=\log_2\left(x-1\right)+3$$  

• x = -1

• x = 1

• x = 3

• x = -3

Multiple Choice

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Multiple Choice

What is the asymptote for the logarithmic function

$$f\left(x\right)=\log\left(x-1\right)$$  

• x=1

• x=-1

• y=1

• y=-1

Multiple Choice

What is the transformation of the logarithmic function
$$f\left(x\right)=\log\ \left(x+3\right)-1$$  

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1