Unit 2b Rational Functions - Review (2024)

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, typically in the form \( f(x) = \frac{P(x)}{Q(x)} \), where \( P(x) \) and \( Q(x) \) are polynomials.

Front

What is the vertical asymptote of a rational function?

Back

The vertical asymptote of a rational function occurs where the denominator is equal to zero and the function approaches infinity.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote describes the behavior of a rational function as \( x \) approaches infinity. It can be determined by comparing the degrees of the numerator and denominator.

Front

How do you find the vertical asymptote of \( f(x) = \frac{2x^2 + 13x + 7}{x + 5} \)?

Back

Set the denominator equal to zero: \( x + 5 = 0 \) which gives \( x = -5 \). Thus, the vertical asymptote is at \( x = -5 \).

Front

How do you find the horizontal asymptote of \( f(x) = \frac{2x^2 + 13x + 7}{x + 5} \)?

Back

Since the degree of the numerator (2) is greater than the degree of the denominator (1), there is no horizontal asymptote.

Front

What is end behavior in the context of rational functions?

Back

End behavior refers to the behavior of the graph of a function as \( x \) approaches positive or negative infinity.

Front

What does it mean if a rational function has a horizontal asymptote at \( y = 5 \)?

Back

It means that as \( x \) approaches infinity or negative infinity, the value of the function approaches 5.

Front

Rewrite \( \frac{2x^2 + 13x + 7}{x + 5} \) in equivalent form.

Back

The equivalent form is \( 2x + 3 + \frac{-8}{x + 5} \).

Front

What is the significance of the coefficients in a rational function?

Back

The coefficients in a rational function affect the shape and position of the graph, including the steepness and direction of the asymptotes.

Front

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

Back

To find the x-intercepts, set the numerator equal to zero and solve for \( x \).