Q. 39 - Precalculus Enhanced with Graphing Utilities

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, or the origin.

Step-by-Step Solution

Answer

(a).   Intercepts points -

• 1 tick to the right (2, 0) 
• 1 tick to the left (-2, 0)
• without moving from the origin (0, 0)

 

(b).  The graph is symmetric with respect to the origin.

Part(a). Step 1. Given data

Graph of an equation is given

Part(a). Step 2. To Find

Find the intercepts. 

Part(a). Step 3. Explanation

Finding the intercepts - 

Intercepts are the values of x and y, when the graph crosses or touch the coordinate axis.

• 1 tick to the right (2, 0) 
• 1 tick to the left (-2, 0)
• without moving from the origin (0, 0)

Part(b). Step 1. Given Data

Graph of an equation is given

Part(b). Step 2. To Find

Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

Part(b). Step 3. Explanation

If the graph is symmetric with respect to the x - axis, It must have points (x, -y) for every (x, y).

Thus, the graph is not symmetric with respect to the x-axis since there is no reflection about the x-axis.

If the graph is symmetric with respect to the y - axis, It must have points (-x, y) for every (x, y).

Thus, the graph is not symmetric with respect to the y-axis since there is no reflection about the y-axis.

The coordinates of a graph that is symmetric with respect to the origin have their counterpart points whose signs are opposite. Illustratively, the graph has a mirror image on the x-axis of its reflection on y-axis.

Thus, The graph is symmetric with respect to the origin.