Finding Domain and Range of Rational Functions

What defines a function in terms of its input and output?

• Inputs and outputs are unrelated

• Each input maps to exactly one output

• Each output maps to exactly one input

• Each input maps to multiple outputs

What happens when the degree of the numerator is less than the degree of the denominator in a rational function?

• There is no asymptote

• The function is undefined

• There is a horizontal asymptote at y=0

• There is a vertical asymptote

How do you determine the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

• There is no horizontal asymptote

• It depends on the function's coefficients

• y equals the quotient of the leading coefficients

• y equals zero

How do you find the domain of a function with a denominator of x^2 - 9?

• Set x^2 - 9 equal to zero and solve for x

• Set x^2 - 9 less than zero

• Set x^2 - 9 greater than zero

• Multiply x^2 by -9

What indicates a vertical asymptote in a function's graph?

• When the numerator equals zero

• When the denominator equals zero

• When the numerator is greater than the denominator

• When the graph crosses the y-axis

What is the range of a function whose graph does not cross its horizontal asymptote?

• y is equal to 1

• y is less than or equal to 0 or greater than 1

• All positive numbers

• All real numbers

For a function with a square root in the denominator, what condition must the inside of the square root meet for the domain?

• It must be equal to zero

• It must not equal zero

• It must be greater than zero

• It must be a perfect square

What is the domain of a function with a denominator that can't be zero?

• All real numbers

• All real numbers except where the denominator is zero

• Only positive real numbers

• Only negative real numbers

In which interval notation is the domain of a function that is undefined at x=2 and x=-2 represented?

• (-∞, -2) U (-2, 2) U (2, ∞)

• (-∞, 2) U (2, ∞)

• (-∞, -2) U (2, ∞)

• (-∞, ∞)

What is the range of a function whose graph crosses the horizontal asymptote?

• No real numbers

• All negative numbers

• All positive numbers

• All real numbers