Domain and Range and Holes of Rational Functions

Find the domain of the function. f(x) = x³ / x+8

• x cannot equal to 2

• x cannot equal to -2

• x cannot equal to -8

• All real numbers

Find the domain of the function. f(x) = 3x²/ x⁴ - 1

• x cannot equal to 3

• x cannot equal to -1

• x cannot equal to 1

• All real numbers

Which of the following is considered as removable discontinuities?

• intercepts

• holes

• asymptotes

• domains

What is the domain?

• All real numbers except 1/2

• All real numbers

• All real numbers except -4

• All real numbers except 4

What are the domain and range?

• D: (−∞, 0) ᴜ (0, ∞)

  R: (−∞, 5) ᴜ (5, ∞)

• D: (−∞, 5) ᴜ (5, ∞)

  R: (−∞, 0) ᴜ (0, ∞)

• D: (−∞, 0) ᴜ (0, ∞)

  R: (−∞, −5) ᴜ (−5, ∞)

• D: (−∞, −5) ᴜ (−5, ∞)

  R: (−∞, 0) ᴜ (0, ∞)

What is the point of discontinuity?

• x = -3

• (-3,2)

• x = -5

• (3,8)

What creates a hole in the graph of a rational function?

• Crossing the x-axis

• An absence of dirt.

• Crossing a vertical asymptote.

• A factor that cancels out.

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: x = -3;

  VA: x = 1

• Holes: x = -3, 1

  VA: None

• Holes: x = 1

  VA: x = -3

What is the DOMAIN?

• All Real Numbers