Question

question 16, 2.2.49 part 2 of 3 the graph of an equation is shown on the right. (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. the x - intercept(s) is/are. (type a whole number. use a comma to separate answers as needed.) b. the graph touches the x - axis on the interval -3,-1. (type your answer in interval notation.) c. the graph has no x - intercepts. find the y - intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the graph touches the y - axis on the interval. (type your answer in interval notation.) b. the y - intercept(s) is/are. (type an integer or a decimal. use a comma to separate answers as needed.) c. the graph has no y - intercepts.

Explanation:

Step1: Find x - intercepts

The x - intercepts are the points where the graph crosses or touches the x - axis (where y = 0). From the graph, we can see that the graph crosses the x - axis at x=-3. So the x - intercept is - 3.

Step2: Find y - intercepts

The y - intercepts are the points where the graph crosses or touches the y - axis (where x = 0). From the graph, we can see that the graph crosses the y - axis at y = 2. So the y - intercept is 2.

Step3: Check for symmetry

• x - axis symmetry: If (x,y) is on the graph, then (x, - y) should be on the graph. Looking at the graph, if we take a point (x,y) on the graph, the point (x, - y) is not on the graph. So it is not symmetric about the x - axis.
• y - axis symmetry: If (x,y) is on the graph, then (-x,y) should be on the graph. Looking at the graph, if we take a non - zero x value for a point (x,y) on the graph, the point (-x,y) is not on the graph. So it is not symmetric about the y - axis.
• origin symmetry: If (x,y) is on the graph, then (-x,-y) should be on the graph. Looking at the graph, if we take a point (x,y) on the graph, the point (-x,-y) is not on the graph. So it is not symmetric about the origin.

Answer:

(a)
A. The x - intercept(s) is/are - 3.
B. The y - intercept(s) is/are 2.
(b) The graph is symmetric with respect to none of these.