1. ## Functions

Given f(x)=8x^3, sketch the graph of g(x) in detail, where g(x)=f(x - 1)+1

Im unsure what to do!
do you sub in f(x) or...??

2. Originally Posted by scubasteve94
Given f(x)=8x^3, sketch the graph of g(x) in detail, where g(x)=f(x - 1)+1

Im unsure what to do!
do you sub in f(x) or...??
Since $\displaystyle f\!\left(x\right)=8x^3$, and $\displaystyle g\!\left(x\right)=f\!\left(x-1\right)+1$, this means that $\displaystyle g\!\left(x\right)=8\left(x-1\right)^3+1$.

All that you're doing with $\displaystyle f\!\left(x\right)$ is shifting it over one unit to the right (which is what $\displaystyle f\!\left(x-1\right)$ represents) and then shifting it up one unit (which is what $\displaystyle f\!\left(x-1\right)+1$ represents).

Does this make sense?

3. Yes i think so but what does the 8 do??

4. Originally Posted by scubasteve94
Yes i think so but what does the 8 do??
You can think of it as a vertical stretch. It takes the values of the function $\displaystyle x^3$ and multiplies them by 8.

5. so is it just the dilation factor??

6. Originally Posted by scubasteve94
so is it just the dilation factor??
Yes.

7. Thank you very much