Domain, Range, Zeros and Holes of a Rational Function

• A hole when x = 4  No Zeros

• A hole when x =- 4   Zeros when: x = -3 and x = -7

• A hole when x = 4   Zeros when: x = -3 and x = -7

• A hole when x = 4   Zeros when x = 3 and x = 7

What is the domain and range of this rational function?

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

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

State the Domain and Range.

• D:  x ≠ 5 , and  R:  y ≠ 7

• D:  x ≠ -5 , and  R:  y ≠ 7

• D:  x ≠ 5 , and  R:  y ≠ -7

• D:  x ≠ 7 , and  R:  y ≠ 5

What's the vertical asymptote of the function?

• x = -9

• x = 9

• x = 3 , x = -3

• x = 3

Is there a hole on the graph of the function?

• Yes when x = 2

• Yes when x = -2

• No there are no holes.

• Yes when x = 5

What is the domain and range?

Find the vertical asymptote(s).

• x = 3 and x = -7

• x = 3

• x = -7

• x = -4