Math 3 Unit 4 Lesson 1 Review

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at values of x that make both the numerator and denominator equal to zero, indicating that the function is undefined at that point.

Front

How do you identify holes in the graph of a rational function?

Back

To identify holes, factor both the numerator and denominator, then find common factors. The x-values that make these common factors zero are the locations of the holes.

Front

What is a rational function?

Back

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

What is a horizontal asymptote?

Back

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

Front

How do you find horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, divide the leading coefficients.

Front

What are x-intercepts?

Back

X-intercepts are points where the graph of a function crosses the x-axis, occurring when f(x) = 0.

Front

How do you find 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 the leading coefficient in a rational function?

Back

The leading coefficient affects the end behavior of the graph of the function, influencing whether it rises or falls as x approaches infinity.

Front

What is the difference between a hole and a vertical asymptote?

Back

A hole indicates a point where the function is undefined but can be removed from the graph, while a vertical asymptote indicates a value where the function approaches infinity.