Finding the Domain for Rational Functions Expressions

What is an excluded value?

• A value that makes the denominator equal to 0

• A number that makes the numerator equal to 0

• The solution

• An ostracized number

State the excluded values. x ≠ ?

• A

• B

• C

• D

State the excluded values. x ≠ ?

• A

• B

• C

• D

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• Hole: x = 1
  VA: x = -3/2
  Domain: (-∞, -3/2)U(-3/2, 1)U(1, ∞)

• Hole: x = 1
  VA: x = 3/2
  Domain: (-∞, 3/2)U(3/2, 1)U(1, ∞)

• Hole: x = -3/2
  VA: x = 1
  Domain: (-∞, -3/2)U(-3/2, 1)U(1, ∞)
  

• Hole: x = 4
  VA: x = -1/3
   Domain: (-∞, -1/3)U(-1/3, 4)U(4, ∞)

• Hole: x = -1/3
  VA: x = 4 
  Domain: (-∞, -1/3)U(-1/3, 4)U(4, ∞)

• Hint: Factor the numerator by using difference of squares and factor the denominator by using the x- method.

Where is the hole?

• x= 4

• x= -4

• x= 5

• x= -5

What (if any) holes exist?

• x=2

• x=2 and x=3

• x=-3

• x=3

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