Pre-Calculus Homework - Section 2.5 Part B: Rational Functions

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It indicates that the function is undefined at that point.

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. The values of x that make the denominator zero are the vertical asymptotes.

Front

What does @@ ext{lim}_{x ightarrow a^+} f(x) = + ext{infty} @@ mean?

Back

It means that as x approaches a from the right, the function f(x) increases without bound.

Front

What does @@ ext{lim}_{x ightarrow a^-} f(x) = - ext{infty} @@ indicate?

Back

It indicates that as x approaches a from the left, the function f(x) decreases without bound.

Front

What is end behavior in the context of rational functions?

Back

End behavior describes how a function behaves as x approaches positive or negative infinity. It helps in understanding the horizontal asymptotes.

Front

How do you determine the end behavior of a rational function?

Back

To determine end behavior, analyze the degrees of the numerator and denominator. Compare their leading coefficients to find horizontal asymptotes.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the graph of a function approaches as x approaches infinity or negative infinity.

Front

What is the significance of x-intercepts in a rational function?

Back

X-intercepts are points where the function crosses the x-axis, indicating the values of x for which f(x) = 0.

Front

How do you find the x-intercepts of a rational function?

Back

To find x-intercepts, set the numerator of the rational function equal to zero and solve for x.

Front

What is the significance of y-intercepts in a rational function?

Back

Y-intercepts are points where the function crosses the y-axis, indicating the value of f(x) when x = 0.