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.) b. there are no intercepts.

Explanation:

Step1: Find x - intercept

The x - intercept is the point where the graph crosses the x - axis (y = 0). From the graph, the graph crosses the x - axis at x = 2. So the x - intercept is the point (2,0). There are no y - intercepts as the graph does not cross the y - axis.

Step2: Determine symmetry

1. 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. For this graph, if we consider a general point (x,y) on the graph, when we replace y with - y, the graph has the same shape above and below the x - axis, so it is symmetric about the x - axis.
2. 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. The graph does not have the same shape to the left and right of the y - axis, so it is not symmetric about the y - axis.
3. 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. Since the graph is not symmetric about the y - axis, it is not symmetric about the origin.

Answer:

(a) A. The intercept(s) of the graph are (2,0)
(b) The graph is symmetric with respect to the x - axis.