Chapter 1.2, Problem 52E

To determine

To find:The graph of the given equation.

Answer to Problem 52E

The graph of the given equation is shown in Figure-1.

Explanation of Solution

Given information:

Theequation is $y=\sqrt{1-x}$ .

Calculation:

Consider the equation.

  $y=\sqrt{1-x}$

The $x$ intercept is,

  $\begin{array}{l}0=\sqrt{1-x}\\ x=1\end{array}$

The $y$ intercept is,

  $\begin{array}{l}y=\sqrt{1-0}\\ y=0\end{array}$

The $x$ intercept is $\left(1,0\right)$ and the $y$ intercept is $\left(0,1\right)$ .

For symmetry about $y$ axis substitute $x=-x$ , then we get $y=\sqrt{1+x}$ .

For symmetry about $x$ axis substitute $y=-y$ , then we get $-y=\sqrt{1-x}$ .

For symmetry about the origin substitute $x=-x,y=-y$ , then we get $-y=\sqrt{1+x}$ .

Since, none of the above condition result in the equivalent equation.

Thus, the equation is not symmetric.

The graph is shown below.

  

Figure-1