Graphing Rational Functions

When does a slant (oblique) asymptote occur?

• when a factor in the numerator cancels out a factor in the denominator

• when the degree of the numerator is the same as the degree of the denominator

• when the degree of the numerator is exactly one larger than the degree of the denominator

• when the degree of the numerator and the denominator are the same

What are the asymptotes?

• x = -3        y = 1  

• x = 3         y = 1

• x = -3        y = -1

• x = 3         y = -1

What is the horizontal asymptote to this function?

• y=4

• y=0

• y=-2

• y=1

Which equation best represents the graph?

What is the domain and range?

• D : All real number x ≠ -3
  R: All real number y≠ 1
• D : All real number x ≠ 1
  R: All real number y≠ -3
• D : All real number x ≠ 3
  R: All real number y≠ 1
• D : All real number x ≠ -1
  R: All real number y≠ 3

What are the x-intercepts?

• x= 2/3
• x= 4, x = -2
• x= -8, x = 1
• x= -4, x = 2

What (if any) holes exist?

• x=2

• x=2 and x=3

• x=-3

• x=3

What is the vertical asymptote? 

• x = 2

• y = 2

• x = 1

• y = 1

The horizontal asymptote equals zero when:

• the exponents in the numerator and denominator are equal

• the exponent in the numerator is less than the denominator

• the exponent in the numerator is greater than the exponent in denominator

• the numerator equals zero

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

• vertical
• horizontal
• slant
• none