91Ó°ÊÓ

Equation -$y=\sqrt[5]{x}$

Find the intercept point and test for symmetry.

To find the x-intercepts, replace y with 0 and solve for x.

$y=\sqrt[5]{x}$

(0,0) is the x-intercept.

Put $x=0$

$0=\sqrt[5]{x}$

$x=0$

To find the x-intercepts, replace x with 0 and solve for y.

$y=\sqrt[5]{x}$

Put $x=0$

$y=\sqrt[5]{0}$

$y=0$

(0,0) is the x-intercept.

• Checking symmetry about x-axis

if replacing (y) with (-y) leaves the equation unchanged, the graph will be symmetric about the x-axis.

we will start with original equation -

$y=\sqrt[5]{x}$

Replacing (y) with (-y) gives us -

$(-y)=\sqrt[5]{x}$

$y=-\left(\sqrt[5]{x}\right)$

This is not the same as the original equation, the graph will not be symmetric about the x-Axis.

• Checking symmetry about y-axis

if replacing (x) with (-x) leaves the equation unchanged, the graph will be symmetric about the y-axis.

we will start with original equation -

$y=\sqrt[5]{x}$

Replacing (x) with (-x) gives us -

$y=\sqrt[5]{(-x)}$

$y=-\left(\sqrt[5]{x}\right)$

This is not the same as the original equation, the graph will not be symmetric about the y-Axis.

• Checking symmetry about the origin

if replacing (x) with (-x) and (y) with (-y)leaves the equation unchanged, the graph will be symmetric about the origin.

we will start with original equation -

$y=\sqrt[5]{x}$

Replacing (x) with (-x) and (y) with (-y) gives us -

$(-y)=\sqrt[5]{(-x)}$

$-y=-\sqrt[5]{x}$

$y=\sqrt[5]{x}$

This is same as the original equation, the graph will be symmetric about the origin.

The graph of equation $y=\sqrt[5]{x}$will be -