Rational Functions

Front

What is a rational function?

Back

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSA.APR.D.6

Front

What is the parent function of rational functions?

Back

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D