Question

complete parts a. and b. below.

x	y
-2	-10
-1	-3
0	-2
1	-1
2	6
3	25

(type integers or simplified fractions. type n if the function is undefined.)
use the graphing tool to graph the function $y = x^3 - 2$ to the right.
click to enlarge graph

Explanation:

Step1: Verify table values

For each $x$, calculate $y=x^3-2$:

• $x=-3$: $(-3)^3 - 2 = -27 - 2 = -29$
• $x=-2$: $(-2)^3 - 2 = -8 - 2 = -10$
• $x=-1$: $(-1)^3 - 2 = -1 - 2 = -3$
• $x=0$: $0^3 - 2 = 0 - 2 = -2$
• $x=1$: $1^3 - 2 = 1 - 2 = -1$
• $x=2$: $2^3 - 2 = 8 - 2 = 6$
• $x=3$: $3^3 - 2 = 27 - 2 = 25$

Step2: Plot points for graph

Mark the points $(-3,-29), (-2,-10), (-1,-3), (0,-2), (1,-1), (2,6), (3,25)$ on the coordinate grid, then draw a smooth curve connecting them.

Answer:

1. The given table values are all correct for $y=x^3-2$.
2. The graph is a smooth cubic curve passing through the points $(-3,-29), (-2,-10), (-1,-3), (0,-2), (1,-1), (2,6), (3,25)$.