Chapter 3.1, Problem 11CFU

To determine

To find: whether graph of equation is symmetric with respect to x-axis, y-axis, both, or neither; and use information to graph the relation.

Answer to Problem 11CFU

Symmetric with y-axis

  

Explanation of Solution

Given information:

  $y=\sqrt{2-x^2}$

Calculation:

Put $\left(a,b\right)$ into the equation and solve as follows:

  $\begin{array}{l}y=\sqrt{2-x^2}\\ b=\sqrt{2-a^2}\end{array}$

If the solution of equation is same as that of any other case, then their graphs are symmetric.

Let’s check whether the given cases are symmetric with the given equation or not by substituting replacing $\left(x,y\right)$with different coordinates in the equation and simplify as shown below.

Check symmetry with	$\left(x,y\right)$	$y=\sqrt{2-x^2}$	Symmetric with graph equation (Yes/No)
x-axis	$\left(a,-b\right)$	$-b=\sqrt{2-a^2}$	No
y-axis	$\left(-a,b\right)$	$\begin{array}{l}b=\sqrt{2-{\left(-a\right)}^2}\\ b=\sqrt{2-a^2}\end{array}$	Yes

Thus the graph of equation is symmetric with y-axis. The relation is graphed as shown below.