Remediation 3.3 CFA

Vocabulary

• Asymptote: A line that a function approaches

• Domain: The set of all x-values. (Look left and right)

• Range: The set of all y-values (Look down and up)

The parent graph, log₂​(x)

The transformed graph,

log₂​(x+3)

Which way did the graph move? Where is the asymptote?​

​what is the h-value for the red graph?

The asymptote, h

​

Multiple Choice

Logarithmic functions are the inverse of...

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

Multiple Choice

Logarithmic functions have a restricted _____________.

• domain

• range

Multiple Choice

Exponential functions have a restricted ______________.

• domain

• range

Multiple Choice

Classify the following graph.

• Exponential Growth
• Exponential Decay
• Logarithmic

Multiple Choice

Classify the following graph.

• Exponential Growth
• Exponential Decay
• Logarithmic

Multiple Choice

What is the domain?

• $$\left(-\infty,\infty\right)$$

• $$\left(0,\infty\right)$$

• $$\left(-\infty,0\right)$$

Multiple Choice

What is the domain?

• (-∞, ∞)
• (0, ∞)
• [1, ∞)
• (1, ∞)

Multiple Choice

What is the range of the function?

• $$\left(0,\ \infty\right)$$

• $$\left(-\infty,0\right)$$

• all real numbers

Multiple Choice

What is the range of log(x)?

• (-2, 4)
• (-∞, ∞)
• (-∞, 0)
• Cucumber

Multiple Choice

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

• $$\left(-\infty,\infty\right)$$  

• $$\left(2,\infty\right)$$  

• $$\left(-2,\infty\right)$$  

• $$\left(-\infty,2\right)$$  

Multiple Choice

What is the asymptote for the equation $$y=2^{x+5}-7$$  ?

• y = -7

• y = 7

• y = 5

• x = 2

Multiple Choice

A given exponential function has an asymptote at y=12. What must be the asymptote of the inverse?

• $$y=\frac{1}{12}$$

• $$x=12$$

• $$x=-12$$

• $$y=-12$$

Multiple Choice

A given logarithmic function has an asymptote at x=5. What must be the asymptote of the inverse?

• 
  

  $$x=\frac{1}{5}$$  

• $$y=\frac{1}{5}$$  

• $$x=5$$

• $$y=5$$

Multiple Choice

Identify the asymptote of the transformed graph $$\log_2\left(x+3\right)$$  shown in red in the graph

• $$x=-3$$  

• $$x=3$$  

• $$y=3$$  

• $$y=-3$$  

We will focus on what a, h, and k do to affect the parent function

​

​Transformations of Logs

Exponential Transformations

Multiple Choice

What are the transformations of this graph?

• Right 1 Up 5
• Right 1 Down 5
• Left 1 Up 5
• Left 1 Down 5

Match

Match the following log functions to their horizontal shift (which way will the asymptote shift)

• $$\ln\left(x\right)$$  

• $$\ln\left(x-4\right)$$  

• $$\ln\left(x+5\right)$$  

No Horizontal Shift

Shift Right

Shift Left

• No Horizontal Shift

• Shift Right

• Shift Left

Multiple Choice

Which of the equations could best describe the graph?

• $$\log_2\left(x+1\right)$$  

• $$\log_2\left(x-1\right)$$  

• $$\log_2\left(x\right)+1$$  

• $$\log_2\left(x\right)-1$$  

Multiple Choice

Which graph matches this equation?

Multiple Choice

Which equation matches this graph?

Multiple Choice

Select the correct graph shape for the equation

$$y=-2\log\left(x+3\right)-1$$

Multiple Choice

Select the correct graph shape for the equation

$$y=-2\cdot10^{\left(x+3\right)}-1$$

Multiple Choice

What is domain of this function?

• $$\left(-\infty,\infty\right)$$

• $$\left(0,\ \infty\right)$$

• 3