Intro to Graphing Rational Functions

Front

What is a rational function?

Back

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.

Front

How do you find the vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided that the numerator is not also zero at those points.

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all possible output values (y-values) that the function can produce, which can be determined by analyzing the function's behavior and asymptotes.

Front

What is a hole in the graph of a rational function?

Back

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

Front

How do you graph a rational function?

Back

1. Identify the domain and vertical asymptotes. 2. Find the x-intercepts and y-intercepts. 3. Determine horizontal asymptotes. 4. Plot points and sketch the graph considering asymptotic behavior.

Front

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

Back

X-intercepts are the points where the graph crosses the x-axis, found by setting the numerator equal to zero.

Front

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

Back

Y-intercepts are the points where the graph crosses the y-axis, found by evaluating the function at x=0.