Q. 43 - Precalculus Enhanced with Graphing Utilities

Question

Draw a complete graph so that it has the type of symmetry indicated.

• the origin

Step-by-Step Solution

Answer

Plot the point (0, 0), $(-\frac{\mathrm{\pi }}{2},-2)$, and $(-\mathrm{\pi },0)$ and draw a smooth curve through them.

Step 1. Given Data

Graph - 

Step 2. To Find

Draw a complete graph so that it has the type of symmetry indicated.

Step 3. Explanation

• Note that (-a, -b) is reflection of (a, b) in the origin.
• When we reflect the point (0, 0) in the origin, We get (0, 0).
• When we reflect the point $(\frac{\mathrm{\pi }}{2},2)$ in the origin, we simply get $(-\frac{\mathrm{\pi }}{2},-2)$.
• when we reflect the point $(\mathrm{\pi },0)$ in the origin, we get $(-\mathrm{\pi },0)$.

Step 4. Final Answer

Plot the point (0, 0), $(-\frac{\mathrm{\pi }}{2},-2)$, $(-\mathrm{\pi },0)$ and  and draw a smooth curve through them.