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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.
Start with the (x+4) part. That means the graph is translated 4 places to the left. Then the -8 part means that it start -8 blocks down, when you set x = -4, the y value is -8. The 3 means that it's getting larger faster.
That is to the power of 6 by the way, I meant to put the little carrot in so it's: f(x) = –3(x + 4)^6 – 8
@carina98 yes, my answers still stays the same. Except for the -3 part. It get's flipped upside down. Didn't see the negative the first time i read it.
Okay so we are just explaining how the graph would appear with the given function? I don't necessarily understand what it means by " how it is related to the graph of x^6"
Overall, start by shifting 4 units left, and 8 units down. Then you flip it upside down because it's negative. Then the graph gets larger quicker because of the 3.
Don't have to worry about the x^6 part because it's simply asking what happens to the graph.
Okay I have it graphed and I am looking at it. So I would just be explaining the change that I notice for my answer?
Yes. You should also study a bit what the numbers do to the function. That way when another problem like this emerges, you'll be able to solve that one too.
Okay awesome so the graph will be pointing downwards?
Yes. The negative sign does that part.
Okay thank you so much for walking me through this I was a bit stuck.
No problem. Glad I could help.
Thank you again! ♥