Chapter 1, Problem 46RE

To determine

To sketch:the graph of the given equation

Answer to Problem 46RE

The equation is not symmetric and the points to locate the graph is $\left(0,0\right)$ , $\left(1,1\right)$ , $\left(2,\sqrt{2}\right)$ , $\left(3,\sqrt{3}\right)$ , $\left(4,2\right)$ , $\left(5,\sqrt{5}\right)$

  

Explanation of Solution

Given:

  $y=\sqrt{x}$

Calculation:

X-axis: To test for symmetry with respect to x-axis, replace y by −y in the equation.

Since, $-y=\sqrt{x}$ is not equivalent to $y=\sqrt{x}$ . The graph is not symmetric with respect to the x-axis.

Y-axis: To test for symmetry with respect to y-axis, replace x by −x in the equation.

Since, $y=\sqrt{-x}$ is not equivalent to $y=\sqrt{x}$ . The graph is not symmetric with respect to the y-axis.

Origin: To test for symmetry with respect to origin, replace x by −x and y by −y, since, $-y=\sqrt{-x}$ is equivalent to $y=\sqrt{x}$ . The graph is not symmetric with respect to the origin.

To graph by hand, use the equation to obtain several points on the graph. The points are given below in tabular form.

$x$$y=\sqrt{x}$ points

$0$ $0$$\left(0,0\right)$   $1$$1$$\left(1,1\right)$   $2$ $\sqrt{2}$$\left(2,\sqrt{2}\right)$   $3$ $\sqrt{3}$ $\left(3,\sqrt{3}\right)$   $4$ $2$ $\left(4,2\right)$   $5$ $\sqrt{5}$ $\left(5,\sqrt{5}\right)$

To graph the equation $y=\sqrt{x}$ using graphical utility, plot all the points as listed in table and connect them to obtain the graph of equation.

The graph of $y=\sqrt{x}$ is given below;

  

Conclusion:

Therefore, the equation is not symmetric and points to locate the graph is $\left(0,0\right)$ , $\left(1,1\right)$ , $\left(2,\sqrt{2}\right)$ , $\left(3,\sqrt{3}\right)$ , $\left(4,2\right)$ , $\left(5,\sqrt{5}\right)$