#50 Graphing Log Functions

Which type of function has a horizontal asymptote?

• exponential

• logarithm

• both

• neither

Which type of function has a vertical asymptote?

• exponential

• logarithm

• both

• neither

Identify the asymptote of the function  $f\left(x\right)=\log_5\ \left(x-1\right)$ .

• x = 5

• x = -1

• y = 0

• x = 1

What are the domain and range of the function  $f\left(x\right)=\log_2x$ ?

• D:  $\left(-\infty,\ \infty\right)$  
  R:  $y>0$  

• Domain:  $\left(-\infty,\ \infty\right)$  
  Range:  $\left(-\infty,\ \infty\right)$  

• Domain:  $x>0$  
  Range:   $\left(-\infty,\ \infty\right)$  

• Domain:  $\left(-\infty,\ \infty\right)$  
  Range:  $y<0$  

Which statement best describes the effects on the graph   $f\left(x\right)=\log_3x$  when it is replaced by $g\left(x\right)=\log_3x+5$ ?

• The graph is horizontally translated 5 units to the right.

• The graph is horizontally translated 5 units to the left.

• The graph is vertically translated 5 units up.

• The graph is vertically translated 5 units down.

Describe the transformations in the logarithmic function  $f\left(x\right)=\log_3x$  to  $g\left(x\right)=4\log_3x+7$ .

• The graph has been translated up 4 units, and left 7 units.

• The graph has been translated left 4 units, and up 7 units.

• The graph has been vertically stretched by a factor of 4, and translated up 7 units.

• The graph has been vertically compressed by a factor of 4, and translated left 7 units.

Describe the transformations in the logarithmic function

 $y=-\log_2\left(x-5\right)$ .

• reflection over the x-axis, right 5 units

• reflection over the x-axis, left 5 units

• vertical compression, down 5 units

• down 1, right 5 units

What equation matches the graph?

• f(x) = log₅(x)

• f(x) = log₁(x)

• f(x) = log₃(x)

What is the equation of the asymptote?

• x = -3
• x=5
• y= -3
• y=5

Match the graph with its equation

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