Q. 36 - 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 -

For x-intercepts -

• 1 tick to the right ( 2,0 )
• 1 tick to the left   ( -2, 0 )

For y-intercepts -

• 1 tick below (0, 3)

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

For x-intercepts -

• 1 tick to the right  ( 2, 0 )
• 1 tick to the left  ( -2, 0 )

For y-intercepts -

• 1 tick below (0, 3)

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. because there is no (0, 3) on the graph.

If the graph is symmetric with respect to the y - axis, It must have points (-x, y) for every (x, y).Illustratively, the graph to the right of y-axis has a mirroring image to the left of y-axis.

Thus, the graph is symmetric with respect to the y-axis since there is ( -2,0 ) for ( 2,0 )

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.