Question

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, the origin, or none of these. (a) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the intercept(s) of the graph are. (type an ordered pair. use a comma to separate answers as needed. use integers or fractions for any numbers in the expression. type each answer only once. type an exact answer, using π as needed.) b. there are no intercepts.

Explanation:

Step1: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis (y = 0). From the graph, the x - intercepts are $(-\pi,0),(0,0),(\pi,0)$.

Step2: Find y - intercepts

The y - intercept is the point where the graph crosses the y - axis (x = 0). From the graph, when x = 0, y = 0, so the y - intercept is (0,0).

Step3: Check for symmetry

• x - axis symmetry: Replace y with -y in the equation of the graph. If the resulting equation is equivalent to the original, the graph is symmetric about the x - axis. Visually, if we reflect the graph about the x - axis, it does not coincide with the original graph, so it is not symmetric about the x - axis.
• y - axis symmetry: Replace x with -x in the equation of the graph. If the resulting equation is equivalent to the original, the graph is symmetric about the y - axis. Visually, the graph is symmetric about the y - axis.
• origin symmetry: Replace x with -x and y with -y in the equation of the graph. If the resulting equation is equivalent to the original, the graph is symmetric about the origin. Visually, if we rotate the graph 180 degrees about the origin, it does not coincide with the original graph, so it is not symmetric about the origin.

Answer:

(a) A. The intercept(s) of the graph are $(-\pi,0),(0,0),(\pi,0)$
(b) The graph is symmetric with respect to the y - axis.