Q. 37 - 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 -

In this case (0, 0) is our intercept for x-axis and y-axis.

 

(b).  The graph is symmetric with respect to x-axis.

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.

In this case (0, 0) is our intercept for x-axis and y-axis.

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) . Illustratively, the graph to the right of x-axis has a mirroring image to the left of x-axis.

Thus, the graph is symmetric with respect to the x-axis since there is ( 0, 0 ) for ( 0, 0 )

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 not symmetric with respect to the origin.