Understanding Rational Functions

What is a rational function?

• A function that is always linear

• A function that is always quadratic

• A function that has no variables

• A function that is a ratio of two polynomials

Why can't the denominator of a rational function be zero?

• Because it would make the function undefined

• Because it would make the function linear

• Because it would make the function quadratic

• Because it would make the function constant

What is the reciprocal function?

• A function that squares its input

• A function that cubes its input

• A function that doubles its input

• A function that pairs each real number with its reciprocal

As x increases, what happens to the y-values of the reciprocal function?

• They oscillate

• They remain constant

• They increase

• They decrease

What is the domain of the reciprocal function?

• All real numbers

• All real numbers except zero

• Only negative numbers

• Only positive numbers

What is the range of the reciprocal function?

• All real numbers except zero

• Only positive numbers

• All real numbers

• Only negative numbers

What is a vertical asymptote?

• A line that the graph never touches

• A line that the graph crosses

• A line that the graph is perpendicular to

• A line that the graph is parallel to

What causes a vertical asymptote in a rational function?

• The numerator being zero

• The function being quadratic

• The denominator being zero

• The function being linear

What is a horizontal asymptote?

• A line that the graph crosses

• A line that the graph approaches as x becomes very large

• A line that the graph is parallel to

• A line that the graph never touches

As x approaches infinity, what happens to the y-values of a rational function with a horizontal asymptote?

• They increase indefinitely

• They approach a specific value

• They decrease indefinitely

• They remain constant