Graphing Rational Functions

Graphing Rational Functions

Horizontal Asymptotes

• https://youtu.be/qAfETdORmcw

Vertical Asymptotes

• https://youtu.be/-jXk1gl_sEo

Y-Intercept

• https://youtu.be/YElHmwdbkzQ

X-Intercepts (Zeros/Roots)

• https://youtu.be/TX_mx3qULpw

Example: Graphing Rational Functions

• https://youtu.be/2N62v_63SBo

Holes

• https://youtu.be/irSg7rstDf0

Domain

• https://youtu.be/5lYSYUmZZ78

Multiple Select

Select ALL the information that applies to the given rational function.
 $f\left(x\right)=\frac{x-3}{-2x^2+8x-6}$  

• Vertical Asymptote. at x = 1

• No Holes

• Horizontal Asymptote. at y = 0

• y-intercept at (0, 1/2)

Multiple Choice

Is there a hole or a vertical asymptote?

• A hole when x = 2

• A vertical asymptote at x = 2

• there is no hole or vertical asymptote

Multiple Choice

What is the domain?

• All real numbers

• All real numbers except 4

• All real numbers except 2

• All real numbers except 2 and -2

Multiple Choice

Find the coordinates of the hole.

• (-3, -3)

• (-3, 3)

• (3, -3)

• (3, 3)

Multiple Choice

Which asymptote(s) are determined by looking at the denominator?

• vertical
• horizontal
• end behavior
• none

Multiple Choice

What is the X-Intercept?

• x= 0
• x= 4
• x= 5
• x= -5

Multiple Choice

The horizontal asymptote equals zero when:

• the degree of the numerator and denominator are equal

• the degree of the numerator is less than the degree of the denominator

• the degree of the numerator is greater than the degree of the denominator

• the numerator equals zero

Multiple Choice

What is the horizontal asymptote of the function?

• y=0
• y=1/3
• none

Multiple Choice

What is the Vertical Asymptote?

• x= -5

• x= 5

• x= 6

• x= -6

Multiple Choice

What are the asymptotes?

• x = -3        y = 1  
• x = 3         y = 1
• x = -3        y = -1
• x = 3         y = -1

Multiple Choice

What are the asymptotes

• x=1, x= 2, y =1, y= 2
• x= 1, x=-1, y = 1
• x=1 y =1
• x=-1, y =1, y =-1

Multiple Choice

What is the Horizontal Asymptote?

• y= 5

• y= -6

• y= 1

• y= 5/-6