Q. 33 - 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 point to the right  (1, 0)
• 1 point to the left   (-1,0)

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

For x-intercepts -

• 1 point to the right  (1, 0)
• 1 point to the left  (-1, 0)

For y-intercepts -

There is no point on the graph that lies on the 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

The graph is symmetric with respect to y - axis since for the point (1, 0) on the graph there is also (-1, 0) which means that the every (x, y) there is (-x, y)

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

Thus, the graph is also symmetric with respect to the origin

If the graph is symmetric with respect to the x-axis, its coordinates and its supposedly counterpart points on its reflection have the exact x-coordinates but their y-coordinates have opposite sign. Illustratively, the graph above the x-axis has a mirroring image below the x-axis.

Thus, the graph is also symmetric with respect to x-axis.