Question

plz help with Your friend hands you a graph of the performance statistics of the newest car to roll off the assembly line. He says, “I know this graph is f(x) = –4(x – 5)3 + 7 but I can’t remember how it is related to the graph of x3.” Explain to your friend how the graph f(x) is a translation of the graph x3.

Answer 1

y=(x)3
Let's try to turn this into the performance function.
Putting a negative in front flips it over the x-axis.
y=−(x)3
To make shifts to the right or up we subtract that value from the corresponding variable.
So we want to shift this function to the right 5 units, so we'll subtract 5 from x.
y=−(x−5)3
We also want to shift this function up by 7, so we'll subtract 7 from y.
y−7=−(x−5)3
Then add 7 to each side,
y=−(x−5)3+7
Then we'll squeeze the function (make it grow four times faster) by multiplying it by 4.
y=−4(x−5)3+7

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