Q. 35 - 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 $(\frac{\mathrm{\pi }}{2},0)$
• 1 tick to the left   $(-\frac{\mathrm{\pi }}{2},0)$

For y-intercepts -

• 1 tick above (0, 1)

(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  $(\frac{\mathrm{\pi }}{2},0)$
• 1 tick to the left  $(-\frac{\mathrm{\pi }}{2},0)$

For y-intercepts -

• 1 tick above (0, 1)
  

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, -1) 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  $(-\frac{\mathrm{\pi }}{2},0)$ for $(\frac{\mathrm{\pi }}{2},0)$

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.