Chapter 1.2, Problem 91AYU

Draw a graph that contains the points $\left(-2,5\right)$, $\left(-1,3\right)$, and $\left(0,2\right)$ that is symmetric with respect to the $y\text{-axis}$. Compare your graph with those of other students; comment on any similarities. Can a graph contain these points and be symmetric with respect to the $x\text{-axis}$? the origin? Why or why not?

To determine

To find: A graph that contains the points $\left(-2,5\right),\left(-1,3\right)$, and $\left(0,2\right)$ that is symmetric with respect to the $y\text{-axis}$. Can a graph contain these points and be symmetric with respect to $x\text{-axis}$ or origin.

Answer to Problem 91AYU

The graph contains these points and is not symmetric with respect to $x\text{-axis}$ or origin.

Explanation of Solution

Given:

The points are $\left(-2,5\right),\left(-1,3\right)$, and $\left(0,2\right)$

Calculation:

It is given that the graph contains the points $\left(-2,5\right),\left(-1,3\right)$, and $\left(0,2\right)$ is symmetric with respect to the $y\text{-axis}$. By the definition of symmetry with respect to $y\text{-axis}$, there exist a point $\left(2,5\right)$ and $\left(1,3\right)$.

The graph contains these points and is not symmetric with respect to $x\text{-axis}$ or origin.