Graphing Logarithms Review

Graphing Logarithms Remediation

By Mrs.Hall

ASYMPTOTES

The ASYMPTOTE is how far LEFT or RIGHT our graph shifts. We can find this value by taking the opposite of the number in the parentheses.

In this case, our asymptote is at x = -3​

​

Multiple Choice

Where is the asymptote?

• x = 1
• y = 1
• x = -1
• y = -1

Multiple Choice

What is the vertical asymptote of the equation  $$y=\log_5\left(x+3\right)+5$$  

• x = -3

• y = -3

• x = 5 

• y = 5

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

The DOMAIN for all logarithmic functions is

(asymptote, ∞).

​

In this case, our domain is (-3, ∞​)

DOMAIN

Multiple Choice

What is the Domain?

• $$\left(0,\infty\right)$$  

• $$\left(-\infty,\infty\right)$$  

• $$\left(1,\infty\right)$$  

• $$\left(-\infty,1\right)$$  

Multiple Choice

What is the domain of the graph  $$y=\log_2\left(x+3\right)+1$$  

• (-1, ∞)

• (-3, ∞)

• (3, ∞)

• (1, ∞)

The RANGE for all logarithmic functions is

(-∞, ∞).

​​

RANGE

Multiple Choice

What is the range of the graph  $$y=\log_2\left(x+3\right)+1$$  

• (∞, -∞)

• (-∞, ∞)

• (-3, ∞)

• (1, ∞)

Left

Right

(The Asymptote)

(Always the opp.)​

h ​

Stretch

Compression

Reflection

(if negative)​

a

TRANSFORMATIONS

alog(x - h) + k​

k ​

Up

Down​

Multiple Select

Select all the transformations that apply.

y = log ₅ (x + 1) +1

• Horizontal shift left 1

• Horizontal shift right 1

• Vertical shift up 1

• Vertical shift down 1

Multiple Choice

What are the transformations for the graph of ? $$y=\log_4\left(x-1\right)+5$$  

• Right 1 Up 5

• Right 1 Down 5

• Left 1 Up 5

• Left 1 Down 5

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

Y-Intercept

Plug zero (0) in for the x-value and evaluate to find the y-intercept.

Multiple Choice

What is the y-intercept of the function   $$y=\log_2\left(x+8\right)+3$$ ? 

• (0, 6)

• (0, 3)

• (0, 8)

• (0, -8)

Multiple Choice

What is the y-intercept of the function: $$f\left(x\right)=2\log\ \left(x\right)-1$$  

• (0, -1)

• None

• (0, 2)

• (0, 10)

Let's put it all together!

Multiple Choice

What is the  Vertical Asymptote?

• x=5
• x=0
• y=0
• x=1

Multiple Choice

What is the Domain?

• $$\left(0,\infty\right)$$  

• $$\left(-\infty,\infty\right)$$  

• $$\left(1,\infty\right)$$  

• $$\left(-\infty,1\right)$$  

Multiple Choice

What is the Range?

• $$\left(0,\infty\right)$$  

• $$\left(-\infty,\infty\right)$$  

• $$\left(1,\infty\right)$$  

• $$\left(-\infty,1\right)$$  

Multiple Choice

What is the range of this graph?

• $$\left(-\infty,\infty\right)$$  

• $$\left(1,\infty\right)$$  

• $$\left(-1,\infty\right)$$  

• $$\left(3,\infty\right)$$  

Multiple Choice

What is the domain of this graph?

• $$\left(-\infty,\infty\right)$$  

• $$\left(1,\infty\right)$$  

• $$\left(-1,\infty\right)$$  

• $$\left(3,\infty\right)$$  

Multiple Choice

What is the equation of the asymptote?

• x = -3
• x=5
• y= -3
• y=5

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