Question

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.

Answer 1

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

Answer 2

I will give you a couple of rules.

Answer 3

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

Answer 4

` ` IF YOU ARE DEALING WITH SOME PARENT
FUNCTION OF X RAISED TO THE POWER OF W. ` `


For any function \(\Large\color{black}{ \displaystyle f(x) = x^{\rm w} }\).
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` 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.
---------------------------------

Answer 5

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.

Answer 6

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.

Answer 7

STEP 1 (your parent function):

\(\LARGE\color{black}{ \displaystyle f(x)=x^6 }\)
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STEP 2:

\(\LARGE\color{black}{ \displaystyle f(x)=\left(x\color{blue}{+4}\right)^6 }\)
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STEP 3:

\(\LARGE\color{black}{ \displaystyle f(x)=\left(x+4\right)^6 \color{blue}{-8} }\)
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STEP 4:

\(\LARGE\color{black}{ \displaystyle f(x)=\color{blue}{3\cdot }\left(x+4\right)^6 -8 }\)
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STEP 5 (the last step):

\(\LARGE\color{black}{ \displaystyle f(x)=\color{blue}{ -}{\tiny~}3\cdot \left(x+4\right)^6 -8 }\)
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Answer 8

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

Answer 9

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

Answer 10

Anytime !