I need help with precal?

Question

y=³√x

I need to find the intercepts algebraically

I asked this question once and people told me to substitute with 0........DUH!!!!

But dont know how to solve this problem because of that small 3

Answer 1

Only intercept is at (0, 0)

looks like y = x³ rotated 90degrees and reflected through the x axis (as these 2 functions are the inverse of each other)

Answer 2

The small 3 would indicate a cube root.

Find the x-intercepts by substituting with 0 for y (Yeah, yeah, duh!)

0 = ³√(x)

To cancel out the cube root (power of 1/3), cube both sides (power of 3).

[ 0 ]³ = [ ³√(x) ] ³

Zero cubed is zero, and the cube of a cube root is x:

0 = x

There's your one x-intercept.

For the y-intercepts, plug in 0 for x:

y = ³√(0)

y = 0

Answer:

x-intercept: ( 0, 0 )

y-intercept: ( 0, 0 )