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 x^6.” Explain to your friend how the graph f(x) is a translation of the graph x^6.

Question

anonymous · Answer

I need help with this asap!

oaktree · Answer

Let's take this piece by piece. Let's start with the -8. What do you think that might do to the graph?

anonymous · Answer

it will make it go down? I'm really confused.

oaktree · Answer

Trust your instincts, they're usually right! The -8 would shift the graph 8 units down.

oaktree · Answer

Now let's tackle the -3. The minus is pretty simple. What do you think that should do? (Think about the graph of $$x^2$$compared to the graph of $$-x^2$$

anonymous · Answer

shift down 3 units?

oaktree · Answer

Not quite. Keep in mind that we're multiplying, not adding. The -3 will flip the graph about the x-axis and make it three times longer.

oaktree · Answer

The minus turns all the positive values to negatives and vice versa, so it'll be a perfect mirror image horizontally. And the 3 makes the graph be three times as "tall". (Keep in mind that this is the same as a graph that is 1/3 as wide.)

oaktree · Answer

Finally (phew!) the +4 in parenthesis. What do you think that will do?

anonymous · Answer

Will it turn to -4?

oaktree · Answer

Not exactly. The +4 will actually shift the graph 4 units to the left. Think of it like this: when you plug in x=0, you will get a value out of it as if it were x=4, right?

oaktree · Answer

So overall, f(x) is the graph of x^6 shifted 4 to the left, then reflected about the x-axis and elongated vertically by a factor of 3, and then finally shifted down by 8 units.

oaktree · Answer

(If you're still confused as to how this all happened, check this website. It'll walk you through the steps. http://www.purplemath.com/modules/fcntrans.htm)

anonymous · Answer

yea I'm still confused.. But Thanks for helping anyways!