Question

question 12, 2.2.41, part 2 of 2. hw score: 21%, 10.5 of 50 points. points: 0 of 1. 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 and, if necessary, fill in the answer box to complete your choice. a. the intercept(s) of the graph are (0,3),(0, - 3) (type an ordered pair. use a comma to separate answers as needed.) b. there are no intercepts. (b) select all that apply. a. the graph is symmetric with respect to the y - axis. b. the graph is symmetric with respect to the origin. c. the graph is symmetric with respect to the x - axis. d. the graph is not symmetric.

Explanation:

Step1: Identify x - and y - intercepts

The x - intercept is the point where the graph crosses the x - axis (y = 0), and the y - intercept is the point where the graph crosses the y - axis (x = 0). Looking at the graph, it crosses the y - axis at (0,3) and (0, - 3), and does not cross the x - axis.

Step2: Check for symmetry

• X - axis symmetry: Replace y with - y in the equation of the graph. If the resulting equation is the same as the original, the graph is symmetric about the x - axis. This graph 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 the same as the original, the graph is symmetric about the y - axis. This 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 the same as the original, the graph is symmetric about the origin. This graph is not symmetric about the origin.

Answer:

(a) A. The intercept(s) of the graph are (0,3),(0, - 3)
(b) A. The graph is symmetric with respect to the y - axis