Questions: The graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "hole Use the graph to complete the following. (a) Find all x-intercepts and y-intercepts. Check all that apply. x-intercept(s): -4 4 -3 0 None y-intercept(s): 0 -3 -4 None (b) 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): x=-3 Horizontal asymptote(s): y=0 (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: Range:

The graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "hole Use the graph to complete the following. (a) Find all x-intercepts and y-intercepts. Check all that apply. x-intercept(s): -4 4 -3 0 None y-intercept(s): 0 -3 -4 None (b) 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): x=-3

Horizontal asymptote(s): y=0 (c) Find the domain and range of f.

Write each answer as an interval or union of intervals. Domain:

Range:

Transcript text: The graph of a rational function $f$ is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "hole Use the graph to complete the following. (a) Find all $x$-intercepts and $y$-intercepts. Check all that apply. $x$-intercept( $(s):$ $-4$ 4 $-3$ 0 None $y$-intercept(s): 0 $-3$ $-4$ None (b) 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): \[ x=-3 \] Horizontal asymptote(s): $y=0$ (c) Find the domain and range of $f$. Write each answer as an interval or union of intervals. Domain: $\square$ Range: $\square$

Solution

Solution Steps

Step 1: Identify x-intercepts and y-intercepts

x-intercepts: The graph crosses the x-axis at $ x = 4 $.
y-intercepts: The graph crosses the y-axis at $ y = -4 $.

Step 2: Determine vertical and horizontal asymptotes

Vertical asymptote: The graph has a vertical asymptote at $ x = -3 $.
Horizontal asymptote: The graph has a horizontal asymptote at $ y = 0 $.

Step 3: Find the domain and range

Domain: The function is defined for all $ x $ except where there is a vertical asymptote. Therefore, the domain is $ (-\infty, -3) \cup (-3, \infty) $.
Range: The function takes all values except where there is a horizontal asymptote. Therefore, the range is $ (-\infty, 0) \cup (0, \infty) $.