Question

Please help soon!

How can the graph of f(x) = ∛x be transformed to represent the function g(x) = ∛-3?

Translate the graph of f(x) ___ 3 units.
Selective options: right, left, up, and down.

The point ____ is on the graph of g(x).
Selective options: (-8,-1), (-1,-2), (2,-1), and (8,-1).

Answer 1

Down, (8,-1)

Explanation:

Answer 2

a) Translate the graph of f(x) down 3 units.

b) (8,-1) is a point on the graph of g(x)

Explanation:

The transformations that subtract a constant number of units from the functional expression f(x) are transformations that lower the graph of the function in those many units,

Therefore they correspond to a translation of the original graph down the number of units involved.

In this case, the number of units involved is "3" (due to the "-3" added to the expression for f(x). So he correct answer for the first part is: Translate the graph of f(x) down 3 units.

For the second part, one has to try each of the coordinate pairs given in the new function g(x) to see which one results in a true statement:

1) Testing (-8,-1) by checking if replacing x with the value "-8" renders "-1" for the y-value:
`g(x)=\sqrt[3]{x} -3\\g(-8)=\sqrt[3]{-8} -3\\g(-8)=-2-3\\g(-8)=-5`

so this is NOT a point on the graph of g(x).

2) Testing (-1,-2) by checking if replacing x with the value "-1" renders "-2" for the y-value:
`g(x)=\sqrt[3]{x} -3\\g(-1)=\sqrt[3]{-1} -3\\g(-1)=-1-3\\g(-1)=-4`

so this is NOT a point on the graph of g(x).

3) Testing (2,-1) by checking if replacing x with the value "2" renders "-1" for the y-value:
`g(x)=\sqrt[3]{x} -3\\g(2)=\sqrt[3]{2} -3\\`

the cubic root of 2 is not a rational number, because 2 is not a perfect cube, so the expression cannot be reduced, so this is NOT a point on the graph of g(x).

4) Testing (8,-1) by checking if replacing x with the value "8" renders "-1" for the y-value:
`g(x)=\sqrt[3]{x} -3\\g(8)=\sqrt[3]{8} -3\\g(8)=2-3\\g(8)=-1`

Therefore this pair (8,-1) IS a point on the graph of g(x).