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

What is a vertical asymptote?

Back

Front

How do you find vertical asymptotes of a rational function?

Back

To find vertical asymptotes, set the denominator equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

Front

How do you determine horizontal asymptotes for rational functions?

Back

Front

What is the significance of the leading coefficient in rational functions?

Back

The leading coefficient affects the end behavior of the function and helps determine horizontal asymptotes.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator equals zero, leading to division by zero.

Front

What is the relationship between the graph of a rational function and its asymptotes?

Back

The graph of a rational function will approach its vertical asymptotes but never touch them, and it may approach horizontal asymptotes as x approaches infinity.

Front

How can you identify the x-intercepts of a rational function?

Back

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