Graphing a cube root function

Question

Graph the function.

Plot five points on the graph of the function, as follows.

1. Plot the first point using the x-value that satisfies
2. Plot two points to the left and two points to the right of the first point.

Answer 1

Cube both sides.

x + 2 = 0

x = -2

(-2,0) is your first point.

If y = -1, what is x? Keep going.

Answer 2

f(x) = cube root of (x+2)

y^3 = x+2

It's the standard graph of y^3=x, but shifted up 3

(-2, 0) is on the graph, but there are no points directly to the left or right, not horizontally.

it's a one to one function, where for any x value there is only 1 y value, and for any y value there is only 1 x value. Draw any vertical or horizontal line through the graph and it only cuts it once.

similarly there are no points vertically up or down from (-2,0)

BUT

f(x) is symmetric about the point (-2,0) so (-1,1) is on the graph which is to the right diagonally

and (-3,-1) is also on the graph, which is to the left, diagonally

just get 2 more points on that diagonal through (-2,0)

(6,2), (-10,-2) among endless other possible points