Question

I need help with #3 pleaseee!!

Answer 1

Explanation:

a)

g(x) = f(-½ x) - 3

the "-" in the function argument flips the function left-right. everything that was for f(x) on the left side of the origin, is now on the right side. and vice versa.

the 1/2 in the function argument stretches out the function left and right by the factor 2.

the "- 3" at the end shifts the whole function down by 3 units.

the new equation :

`g(x) = \sqrt[3]{ - x / 2} \: - 3`

b)

j(x) = 2f(x + 4)

the "+ 4" in the function argument moves the whole function 4 units to the left (everything that happened for f(x) at x happens now 4 units "earlier" - the functional result of f(x + 4) is now created at x).

the factor 2 of f stretches out the whole function up and down (by the factor 2).

the new equation :

`j(x) = 2 * \sqrt[3]{x + 4} \:`

c)

h(x) = f(8x - 24)

the "- 24" in the functional argument moves the whole function 24 units to the right (and principle as in b., now f(x - 24) happens only at x and therefore "later").

the factor 8 in the functional argument compresses (or shrinks) the whole function left and right by the factor 8.

the new equation :

`h(x) = \sqrt[3]{8x \: - 24}`