Question

For the function f(x) = x4 – 8, write the rule for g(x).

g(x) = f(x) + 4

Answer 1

Rule? I think you just replace f(x) in the g(x) function with the whole of f(x). Unless I'm missing what the question wants.

Answer 2

so what would the answer be?

Answer 3

\(\bf \large {f(x) = \color{red}{x^4 - 8}\qquad

g(x) = \color{red}{f(x)} + 4}\)

Answer 4

what do you think?

Answer 5

g(x) = x^4 - 4

Answer 6

yeap, that is correct :)

Answer 7

awesome!

what about this one?
For the function f(x) = x4 – 8, write the rule for h(x).

h(x) = f(x - 2)

Answer 8

h(x) = x^4 - 8 + f(x-2)

Answer 9

\(\bf \large {f(x) = \color{red}{x}^4 - 8\qquad h(x) = f(x - 2)\\ \quad \\

f(\color{red}{x - 2})=(\color{red}{x-2})^4 - 8\Longleftrightarrow h(x)}\)

Answer 10

so overall, what would the new equation be?

Answer 11

I think that's it, you're not expected it to expand it, I don't think

Answer 12

just keep in mind that the argument passed in the function, replaces any "x" in the function itself.... say \(\bf \large{ f(\textit{my sharona})=(\textit{my sharona})^4 - 8\\ \quad \\
f(\textit{cheeseburger with fries}) = (\textit{cheeseburger with fries})^4 - 8}\)

Answer 13

so it is
h(x) = f(x−2)^4−8

Answer 14

see f( x - 2 ) <--- is passing x-2 as the value to replace any "x" in the equation, so you end up with \(\bf f(\color{red}{x - 2})=(\color{red}{x-2})^4 - 8\Longleftrightarrow h(x)\)

Answer 15

For the function f(x) = x4 – 8, write the rule for j(x).

j(x) = f(3x)

Answer 16

f(3x) <--- notice the argument passed now is "3x", so you replace any "x" in the f(x) with 3x

Answer 17

\(\bf \large {f(x) = \color{red}{x}^4 - 8\qquad j(x) = f(3x)\\ \quad \\

f(\color{red}{3x})=(\color{red}{3x})^4 - 8\Longleftrightarrow j(x)}\)

Answer 18

j(x) = 3x^4 - 8

Answer 19

\(\bf (ab)^n\implies a^nb^n\qquad thus (3x)^4\implies 3^4x^4\)