Chapter 1.2, Problem 40AYU

In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the $x\text{-axis}$, the $y\text{-axis}$, or the origin.

To determine

To find: The intercepts and to indicate whether the graph is symmetric with respect to the $x\text{-axis}$, $y\text{-axis}$ and the origin.

Answer to Problem 40AYU

The intercepts are $\left(-4,0\right),\left(0,0\right)$, and $\left(4,0\right)$. The graph is symmetric with respect to the origin.

Explanation of Solution

Given:

The graph of an equation

Calculation:

From the given graph, we can identify that the intercepts are $\left(-4,0\right),\left(0,0\right)$ and $\left(4,0\right)$. The $x\text{-intercepts}$ are $-4$ and 4. The $x\text{-intercepts}$ have $y$ coordinates equal to 0.

If a graph is symmetric with respect to the origin and the point $\left(x,y\right)$ is on the graph then the point $\left(-x,-y\right)$ is on the graph. Also the point $\left(-x,y\right)$ is on the graph then the point $\left(x,-y\right)$ is also on the graph. The given graph is symmetric with respect to the origin.