Rational Functions

Front

What is a rational function?

Back

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a. They occur where the denominator of a rational function is zero.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the graph of a function approaches as x approaches infinity or negative infinity. They indicate the end behavior of the function.

Front

How do you find vertical asymptotes of a rational function?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

How do you find horizontal asymptotes of a rational function?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator: If degree of P < degree of Q, y = 0; if degree of P = degree of Q, y = leading coefficient of P / leading coefficient of Q; if degree of P > degree of Q, no horizontal asymptote.

Front

What is a hole in a graph of a rational function?

Back

A hole occurs in the graph of a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you simplify a rational function?

Back

To simplify a rational function, factor both the numerator and denominator and cancel out any common factors.

Front

What is the parent function of rational functions?

Back

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally and/or vertically without changing its shape.

Front

What is the effect of adding a constant to the numerator of a rational function?

Back

Adding a constant to the numerator shifts the graph vertically, affecting the y-intercept but not the asymptotes.