Question

How do you determine whether the given points (0, 0), (1, 1), (1, -1) are on the graph of the equation `y = x^3 - 2(sqrt{x})`?

Answer 1

Check the points in the eqaution and see if the left site is eqaul to the right side?

Explanation:

`y = x^3 - 2sqrt x, and (0, 0), (1, 1), (1, -1)`:

`(0, 0):`
Is `0 = 0^3 - 2sqrt 0` ?
`0 = 0`

`(1, 1):`
`y = x^3 - 2sqrt x`
Is `1 = 1 - 2sqrt 1` ?
`1 = -1` ? No.

`(1, -1):`
Is `-1 = 1^3 - 2sqrt 1` ?
`-1 = -1`

`(0, 0) and (1, -1)` lie on the graph.

Here is the graph: https://www.desmos.com/calculator/8chclct0c1