List the intercepts and test for sysmmetry

Question

y=3√x

Answer 1

There are two types of intercepts: y-intercept and x-intercept. Y-intercept is where our function crosses the y-axis and X-intercept is where our function crosses the x-axis.

Thus to find Y-intercept: set X=0 and solve for y => y=3(0)=0

To find X-intercept: set Y=0 and solve for x => 0=3√x => x=0

Either way both the X and Y intercepts are (0,0) the origin.

Testing for symmetry involves three tests.

IF f(-x)=f(x) => sym about the y-axis

IF -f(x)=f(x) => sym about the x-axis

IF -f(-x)=f(x) =>sym about the origin

If you further check these three conditions, you'll see the function f(x)=3√x has no symmetry.