## anonymous one year ago PLEASE HELP ILL GIVE A MEDAL Your friend hands you a graph of the engine power statistics of a race car. He says, “I know this graph is f(x) = –3(x + 4)6 – 8 but I can’t remember how it is related to the graph of x6.” Explain to your friend how the graph f(x) is a translation of the graph x6.

1. SolomonZelman

Do you mean, $$\large\color{black}{ \displaystyle f(x) =~ –3(x + 4)^6 – 8 }$$ ?

2. SolomonZelman

I will give you a couple of rules.

3. anonymous

Yes its supposed to be f(x) = –3(x + 4)^6 – 8

4. SolomonZelman

  IF YOU ARE DEALING WITH SOME PARENT FUNCTION OF X RAISED TO THE POWER OF W.   For any function $$\Large\color{black}{ \displaystyle f(x) = x^{\rm w} }$$. --------------------------------  SHIFT LEFT/RIGHT  When you have $$\Large\color{black}{ \displaystyle f(x) = (x + {\rm b})^{\rm w} }$$ then your original function is shifted $$\rm b$$ units to the left. When you have $$\Large\color{black}{ \displaystyle f(x) =(x - {\rm b})^{\rm w} }$$ then your original function is shifted $$\rm b$$ units to the right. --------------------------------  SHIFT UP/DOWN  When you have $$\Large\color{black}{ \displaystyle f(x) =x^{\rm w}+ {\rm b} }$$ then your original function is shifted $$\rm b$$ units up. When you have $$\Large\color{black}{ \displaystyle f(x) =x^{\rm w}- {\rm b} }$$ then your original function is shifted $$\rm b$$ units down. --------------------------------  SCALE FACTOR  When you have $$\Large\color{black}{ \displaystyle f(x) = {\rm b}\cdot (x)^{\rm w} }$$ then, your function is increased/shrinked (depends on whether b>1 or b<1) --------------------------------  REFLECTION ACROSS X-AXIS  When you have $$\Large\color{black}{ \displaystyle f(x) = -x^{\rm w} }$$ then your function is reflected (like a mirror) across the x-axis. ---------------------------------

5. SolomonZelman

Explore it piece by piece and keep referring to my list of rules. I will write the changes out so that you can see, them step by step, and you will just need to identify what exactly is going on.

6. anonymous

ok, l understand those rules, i just don't know how to find out how the graph f(x) is a translation of the graph x6.

7. SolomonZelman

STEP 1 (your parent function): $$\LARGE\color{black}{ \displaystyle f(x)=x^6 }$$ ----------------------------------------------- STEP 2: $$\LARGE\color{black}{ \displaystyle f(x)=\left(x\color{blue}{+4}\right)^6 }$$ ----------------------------------------------- STEP 3: $$\LARGE\color{black}{ \displaystyle f(x)=\left(x+4\right)^6 \color{blue}{-8} }$$ ----------------------------------------------- STEP 4: $$\LARGE\color{black}{ \displaystyle f(x)=\color{blue}{3\cdot }\left(x+4\right)^6 -8 }$$ ----------------------------------------------- STEP 5 (the last step): $$\LARGE\color{black}{ \displaystyle f(x)=\color{blue}{ -}{\tiny~}3\cdot \left(x+4\right)^6 -8 }$$ -----------------------------------------------

8. SolomonZelman

hope this helps.... when you look at my last post, please keep referring to the rules that I posted previously.

9. anonymous

Ok I think I got it, thank you SO much!

10. SolomonZelman

Anytime !