Q. 38 - 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 above (0, 2)
• 1 tick below ( 0, -2)

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

For x-intercepts -

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

For y-intercepts -

• 1 tick above (0, 2)
• 1 tick below (0, -2)

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, 2 ) for ( 0, -2)

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 symmetric with respect to the y-axis since there is (-2 , 0) or   (2,0) 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.