Graphing Logarithmic Functions

Which type of function has a horizontal asymptote?

• exponential

• logarithm

• both

• neither

Tags

CCSS.HSF-IF.C.7D

Which type of function has a vertical asymptote?

• exponential

• logarithm

• both

• neither

Tags

CCSS.HSF-IF.C.7E

Logarithmic functions are the inverse of...

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

The graph of  $y=\log_3\left(x-1\right)+2$  is shown on the coordinate grid.

Which statement about the range and asymptote of the function is true?

• The graph has a range of all real numbers and has a vertical asymptote at x = 1.

• The graph has a range of all real numbers less than 4 and has a vertical asymptote at x = 1.

• The graph has a range of all real numbers and has a horizonal asymptote at y = 4.

• The graph has a range of all real numbers less than or equal to 4 and has a horizontal asymptote at x = 1.

Tags

CCSS.HSF-IF.C.7E

The graph of  $y=\log_3\left(x-1\right)+2$  is shown on the coordinate grid.

Which statement about the domain, y-intercept, and symmetry of the function is true?

• The graph has no y-intercept, a domain of all real numbers greater than 1, and is not symmetrical.

• The graph has a y-intercept located at (1, 0), a domain of all real numbers, and has symmetry across the line x = 1.
  

• The graph has no y-intercept, a domain of all real numbers, and is not symmetrical.
  

• The graph has a y-intercept located at (1, 0), a domain of all real numbers greater than 1, and has symmetry across the line x = 1.
  

Tags

CCSS.HSF-IF.C.7E

• x = 5

• x = -1

• y = 0

• x = 1

Tags

CCSS.HSF-IF.C.7E

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

• x = -3

• x = 5

• y = -3

• y = 5

Tags

CCSS.HSF-IF.C.7E

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:  $y<0$  

What is the domain of the function  $g\left(x\right)=\frac{1}{2}\log_2x$ ?

•  $x>0$  

•  $x<0$  

•  $\left(-\infty,\ \infty\right)$ 

•  $x>\frac{1}{2}$  

What is the range of the function  $f\left(x\right)=\log_2\left(x-4\right)-3$ ?

•  $y>-3$ 

•  $x>0$  

•  $\left(-\infty,\ \infty\right)$ 

•  $y>0$