2.6 Graphing Rational Functions

2.6 Graphing Rational Functions

Multiple Choice

Identify the domain of.....

 $f\left(x\right)=\frac{2x-6}{x^2-7x+12}$  

•  $\left(-\infty,4\right)\cup\left(4,\infty\right)$  
  

•  $\left(-\infty,12\right)\cup\left(12,\infty\right)$  
  

•  $\left(-\infty,3\right)\cup\left(3,4\right)\cup\left(4,\infty\right)$  
  

•  $\left(-\infty,\infty\right)$  
  

Fill in the Blanks

Identify the equation for the vertical asymptote for:

 $f\left(x\right)=\frac{2x-6}{x^2-7x+12}$  

Fill in the Blanks

Identify the x value at which the removable discontinuity occurs:

 $f\left(x\right)=\frac{2x-6}{x^2-7x+12}$  

Multiple Choice

Identify the ordered pair for the x-intercept...

 $f\left(x\right)=\frac{2x-6}{x^2-7x+12}$  

• (3,0)

• (4,0)

• (2,0)

• there isn't an x-intercept

Multiple Choice

Identify the equation of the horizontal asymptote.  

 $f\left(x\right)=\frac{2x-6}{x^2-7x+12}$  

• y=0

• y=2

• y= 1/2

• there isn't a horizontal asymptote

Multiple Select

Identify all of the statements that apply to:

 $g\left(x\right)=\frac{\left(4x+3\right)\left(x-5\right)}{\left(x-5\right)\left(x+1\right)}$  

• There is only one infinite discontinuity.

• The y-intercept is (0,3).

• There is an x-intercept at (5,0).

• The horizontal asymptote is y=4.

• There is an x-intercept at (-3/4, 0).

Multiple Select

Identify all of the statements that apply to:

 $h\left(x\right)=\frac{x^2-36}{x-6}$  

• There are 2 x-intercepts.

• There is a vertical asymptote at x=6.

• The y-intercept is at (0,6).

• There isn't a horizontal asymptote.

• There is a removable discontinuity at x=6.

Multiple Select

Identify all of the statements that apply to:

 $f\left(x\right)=\frac{7}{x^2+9}$  

• The domain is  $\left(-\infty,\infty\right)$  .

• The horizontal asymptote is y=0.

• The graph doesn't have any x-intercepts.

• There is a vertical asymptote at x= -9.

• The graph doesn't have any vertical asymptotes.