Rational Functions Test

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

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

What is the vertical asymptote of the function f(x) = 1/(x^2 - 25)?

Back

x = 5, x = -5 (the vertical asymptotes are found by setting the denominator x^2 - 25 = 0).

Front

What is the vertical asymptote of the function f(x) = 1/(x + 9)?

Back

x = -9 (the vertical asymptote is found by setting the denominator x + 9 = 0).

Front

Simplify the expression (4p^2)/(2p).

Back

2p (divide the numerator and denominator by 2p).

Front

What is the result of dividing (6x^2)/(3x)?

Back

2x (divide the numerator by the denominator).

Front

Multiply the rational expressions (x + 2)/(x - 3) and (x - 3)/(x + 4).

Back

(x + 2)/(x + 4) (the (x - 3) cancels out).

Front

What is the horizontal asymptote of the function f(x) = 3x^2/(2x^2 + 1)?

Back

y = 3/2 (the horizontal asymptote is found by comparing the leading coefficients of the numerator and denominator).

Front

What does it mean if a rational function has no vertical asymptotes?

Back

It means that the denominator does not equal zero for any real number x, indicating the function is defined for all real numbers.

Front

What is the domain of the function f(x) = 1/(x - 4)?

Back

All real numbers except x = 4 (the function is undefined at the vertical asymptote).