Levels 1-3: PC Unit 4-Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values (x) approach positive or negative infinity.

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, the asymptote is y=0. If they are equal, divide the leading coefficients.

Front

What is the vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input values (x) approach a certain value, typically where the function is undefined.

Front

How do you find the vertical asymptote of a rational function?

Back

To find the vertical asymptote, set the denominator equal to zero and solve for x.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all possible output values (y) that the function can produce.

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient affects the end behavior of the graph, particularly the horizontal asymptote.

Front

What is a parabola?

Back

A parabola is a U-shaped graph that represents a quadratic function, typically in the form y = ax^2 + bx + c.