Question

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

Answer 2

Hopefully that helps to explain some of those changes :)