Math 3 - 6.1 - 6.3 Graphing Rational Functions Flashcard PRACTICE

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity. For rational functions, it can often be found by comparing the degrees of the numerator and denominator.

Front

What are the two 'curves' on a Rational Function called?

Back

Branches

Front

Back

The vertical asymptote is at x = 5.

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

What is an asymptote?

Back

An imaginary line that your function never touches.

Front

How do you find the horizontal asymptote of a rational function?

Back

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

Front

What is the significance of vertical asymptotes in rational functions?

Back

Vertical asymptotes indicate values of x where the function is undefined and where the graph will approach infinity.

Front

What does it mean for a function to have branches?

Back

Branches refer to the distinct parts of the graph of a rational function that are separated by asymptotes.

Front

How do you graph a rational function?

Back

To graph a rational function, identify asymptotes, intercepts, and test points in each interval created by the asymptotes.

Front

What is the formula for finding the x-intercept of a rational function?

Back

Set the numerator equal to zero and solve for x.