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.

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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.

Mathematics
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Do you mean, \(\large\color{black}{ \displaystyle f(x) =~ –3(x + 4)^6 – 8 }\) ?
I will give you a couple of rules.
Yes its supposed to be f(x) = –3(x + 4)^6 – 8

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` ` 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. ---------------------------------
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.
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.
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): \(\LARGE\color{black}{ \displaystyle f(x)=\color{blue}{ -}{\tiny~}3\cdot \left(x+4\right)^6 -8 }\) -----------------------------------------------
hope this helps.... when you look at my last post, please keep referring to the rules that I posted previously.
Ok I think I got it, thank you SO much!
Anytime !

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