Question

Use a graphing utility to graph the function.Then use the Horizontal Line Test to determine whether the function is one - to - one on its entire domain and therefore has an inverse function.

Answer 1

Step 1:

The rational function

The rational function graph is two or more parts.

Graph the function using asymptotes and intercepts.

Intercepts are .

Find the asymptotes.

Solve for the zeros of denominator.

Vertical asymptote is .

Since the degree of the numerator is equal to the degree of the denominator,horizontal asymptote is the ratio of the leading coefficient of numerator and denominator.

is horizontal asymptote.

Step 2:

Draw the coordinate plane.

Plot the asymptotes and intercepts of the function and draw the curve.

Draw the horizontal line .

Observe the graph: the horizontal line touches the graph of the function exactly one point.

Therefore, the function is one-to-one.

A function has an inverse function if and only if it is one-to-one.

The function is one-to-one on it's entire domain and therefore has an inverse function.

Solution:

Inverse function exists.