Questions: Finding the intercepts, asymptotes, domain, and range from the graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): Horizontal asymptote(s):

Finding the intercepts, asymptotes, domain, and range from the graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary.

Vertical asymptote(s):

Horizontal asymptote(s):

Transcript text: Finding the intercepts, asymptotes, domain, and range from the graph of a rational function $f$ is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): $\square$ Horizontal asymptote(s): $\square$

Solution

Solution Steps

Step 1: Identify Vertical Asymptotes

Vertical asymptotes occur where the function approaches infinity as the input approaches a certain value. From the graph, we can see that the function has a vertical asymptote at $ x = 1 $.

Step 2: Identify Horizontal Asymptotes

Horizontal asymptotes occur where the function approaches a constant value as the input approaches infinity or negative infinity. From the graph, we can see that the function has a horizontal asymptote at $ y = 1 $.