Question

Can somebody Check These Answers For ME :)
Your friend hands you a graph of the performance statistics of the latest powerboat to be produced. He says, “I know this graph is f(x) = –2(x – 4)3 – 3 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.
My answer - Well when you translate ( x^3 ) downwards you get f(x) = -2(x-4)^3-3. Meaning that f(x) = -2(x-4)^3-3 is a translation of ( x^3 ).

Answer 1

@iGreen @amistre64 @mathmale

Answer 2

Your friend hands you a graph of the performance statistics
of the latest powerboat to be produced.

He says, “I know this graph is f(x) = –2(x – 4)^3 – 3
but I can’t remember how it is related to the graph of x^3.”

Explain to your friend how the graph f(x) is a translation of the graph x3.

You answered - Well when you translate ( x^3 ) downwards you get f(x) = -2(x-4)^3-3. Meaning that f(x) = -2(x-4)^3-3 is a translation of ( x^3 ).

this is not accurate. there are 2 translations involved, and a reflection, and a whatever you call a stretching

Answer 3

refresh to rid the odd marks ...

Answer 4

if we start with a function f(x)

we can see that it is shifted (translated side to side) by h units
f(x-h)

now we also see that it has been stretched by a, and reflected about the x axis:
-a f(x-h)

it has then been shifted (translated up/down) by k units:
-a f(x-h) + k

Answer 5

and since f(x) = x^3 .. then f(x-h) = (x-h)^3