Question

Which table represents points on the graph of h(x) = -x+2?

O
O
X
y
X
y
X
y
X
y
-8
4
-1
3
-2 -1
10
3
-6
2
1
-4 -3
-8
-1
2
0
2
2
70
-2
0
1
1
3
-1
8
10
2
-6
10
-2
80

Answer 1

The third table accurately represents the points for the equation.
(The one starting with -6 X --> 2 Y)

Explanation:

To begin, put in some values for x. If these values match with the table then that table will accurately represent the points on the graph.

Step 1. Write out the Equation

`h(x) = \sqrt[3]{-x+2}`

Step 2. Plug in a Value & Solve

The easiest value to plug in here is -1 (the cube root will be easier with multiples of 3).

`h(x)=\sqrt[3]{-(-1)+2}`

Simplify

`h(x) = \sqrt[3]{1+2}`

`h(x) = \sqrt[3]{3}`

`h(x)=1`

Therefore, when X = -1; h(x) (or y) = 1.

Step 3. Compare to Tables

The first two options show y being a different value than 1 for when x = -1. Therefore, it cannot be either of those.

Step 4. Prove a Table to be Inacurate using Step 2

Do the same thing as Step 2, but use a value from one of the tables. In this case, we will use "-2" from the 4th table.

`h(x)=\sqrt[3]{-(-2)+2}`

Simplify

`h(x)=\sqrt[3]{2+2}`

`h(x)=\sqrt[3]{4}`

The 4th table claims that when x is -2, y is 0. The cube root of 4 is not equal to 0. Therefore, the third table is correct.

Answer 2

The third table, because when you plot the points on a graph, they fall on the function's line.