please Help !!! Fan And 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.

Question

anonymous · Answer

Can you Please Help Me ?? This Is My Final Question And Im Stuck !!

anonymous · Answer

@radar

anonymous · Answer

@phi ?????

phi · Answer

$$ f(x) = –3(x + 4)^6 – 8 $$

compared to $ f(x)= x^6 $

if we put -3 in front of the x^6 , the negative means we "flip it upside down" 
the 3 causes the curve to be "steeper"  (the answer is bigger than if we did not multiply)

replacing x with (x+4)  causes  the "zero"  to be at -4  (in other words, when x=4 in the new version (x+4),  we get (-4+4) = 0
that means the x=0  in the original matches up with x=-4  
in other words, we translated LEFT 4 steps

adding -8 to this  –3(x + 4)^6 – 8 
makes f(x) smaller by -8 as compared to  –3(x + 4)^6
in other words we translated DOWN by 8 steps