Questions: The graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

The graph of an equation is given.
(a) Find the intercepts.
(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

Transcript text: The graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the $x$-axis, the $y$-axis, or the origin.

Solution

Solution Steps

Step 1: Find the x-intercepts.

The graph intersects the x-axis at x = -4 and x = 4. Therefore, the x-intercepts are (-4, 0) and (4, 0).

Step 2: Find the y-intercepts.

The graph intersects the y-axis at y = 0. Therefore, the y-intercept is (0, 0).

Step 3: Determine symmetry.

The graph is symmetric with respect to the x-axis because if you fold the graph along the x-axis, the two halves match. The graph is also symmetric with respect to the y-axis, and the origin.