SOLUTION: 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 grap

Algebra ->  Graphs -> SOLUTION: 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 grap      Log On


   



Question 889659: 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.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can say that the x that your friend used
before is no longer valid. You are giving the
friend a new +x%5B1%5D+ with the relation +x%5B1%5D+=+x+%2B+4+
If +x+=+-4+, then +x%5B1%5D+=+0+
so the graph is shifted left +4+ units
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The +%28+x%5B1%5D+%29%5E6+ gets inverted about the x-axis
and each +f%28x%5B1%5D%29+ gets multiplied by +3+
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Then the graph gets shifted down +8+ units
Here are both functions:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-50%2C+50%2C+x%5E6%2C+-3%2A%28+x%2B4+%29%5E6+-+8+%29+