Logarithmic Functions and Properties

Graphs of Logarithmic Functions

Multiple Choice

Logarithmic functions are the inverse of _________________

• exponential functions

• linear functions

• quadratic functions

• cubic functions

Multiple Choice

Which graph is logarithmic

Domain and Range

Multiple Choice

What is the domain of log(x)?

• (-∞, ∞)

• (-∞, 0)

• (0, ∞)

• (0, 8)

Multiple Choice

What is the Domain?

• x > 0
• All Real Numbers
• x > 1
• x < 1

Multiple Choice

What is the domain?

• (-∞, ∞)
• (0, ∞)
• [1, ∞)
• (1, ∞)

Multiple Choice

What is the Range?

• y > 0
• All Real Numbers
• y > 1
• y < 1

Multiple Choice

Domain of y = log x ?

• All real numbers

• x>0

• x<0

• y>0

Multiple Choice

What is the range of the function graphed?

• (-∞, ∞)

• (-∞, 2] and [2, ∞)

• [2, ∞)

• (-∞, 2]

Multiple Choice

Find the domain and range of:
f(x) = log₂(x)

• D: all real numbers
  R: y > 0
• Domain: all real numbers
  Range: all real numbers
• Domain: x > 0
  Range: all real numbers
• Domain: all real numbers
  Range: y < 0

Multiple Choice

Describe range of the function shown: y=log₂(x+1)

• (-∞,∞)

• (-1,∞)

• (-1,3)

• (∞, -1)

Multiple Choice

Describe domain of the function shown: y=log₂(x+1)

• (-∞,∞)

• (-1,∞)

• (-1,3)

• (∞, -1)

Transformations

Multiple Choice

Which graph matches the logarithmic equation

Multiple Choice

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3

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

Multiple Choice

Describe the transformation of y=ln(x) that would give the graph for y = 7ln(x)

• vertical translation 7 up
• vertical stretch by a factor of 7
• vertical compression by a factor of 7
• horizontal translation 7 left

Multiple Choice

Describe the transformation of y=ln(x) that would give the graph for y = ln(x+7)

• vertical translation 7 up
• vertical translation 7 down
  vertical stretch by a factor of 7
• horizontal translation 7 left
• horizontal translation 7 right

Multiple Select

Which of the following transformations would take f(x)= lnx to g(x)= −ln(x+5)

• reflection over the x-axis

• reflection over the y-axis

• translate right 5

• translate up 5

• translate left 5

Multiple Choice

Match the graph with its equation

• y = log₄ (x)+2
• y = log₄ (x + 2) + 1 
• y = log₄ (x - 1) + 2
• y = log₄ (-x + 2)

Multiple Choice

Match the graph with its equation

• y = log₅ (x + 1) + 1 
• y = log₅ (x - 1) + 1 
• y = log₅ (x²) + 1 
• y = log₅ (x)-1

Multiple Choice

Match the graph with its equation

• y = log₆(-x) + 1
• y = log₆(x − 2) + 1
• y = log₆(x + 2) - 1
• y = log(x-8) + 1

Multiple Choice

Describe the transformations of f(x)= -log₂(x+1)

• left one & y-axis reflection
• right one & y-axis reflection
• left one & x-axis reflection
• right one & x-axis reflection

Multiple Choice

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

• g(x)=log₃(x+6)+4

• g(x)=log₃(x+4)-6

• g(x)=log₃(x-6)+4

• g(x)=3log(x+6)+4

Asymptotes

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

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 kind of asymptotes do logs have?

• horizontal ( y=0)
• vertical (x=0)

Multiple Choice

Find the asymptote of the following: y = log₁₀ x - 6

• x=6
• x=-6
• x= 0
• y=0

Multiple Choice

find the asymptote: y = log₁₀ (x+3)

• x=-3
• x=3
• y=-3
• y=3

Multiple Choice

Where is the asymptote?

• x = 1

• y = 1

• x = -1

• y = -1

Multiple Choice

Which of the following has a vertical asymptote at $$x=4$$  

• $$y=2^x-4$$  

• $$y=\log_2\left(x-4\right)$$  

• $$y=2^x+4$$  

• $$y=\log_2\left(x+4\right)$$  

Multiple Choice

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

• x = -3

• x=5

• y= -3

• y=5