Parent function???

[spacewater]

Identify the parent function \(\displaystyle f\)
Describe the sequence of transformations from \(\displaystyle f\) to \(\displaystyle g\)

\(\displaystyle g(x) = -2(x-5)^3+3\)


What does it mean by "the parent function \(\displaystyle f\)" and " the sequence of transformations" ??

 

[tkhunny]

You should be studying a section on Composite Functions. No?

One for free. Look real hard at you g(x).

Parent Function: f(x) = x-5 -- Why did I picl that.
First Transformation: h(x) = x^3
Second Transformation: r(x) = -2x
Third Transformation: s(x) = x+3

Where does that leave us?

 

[Deleted member 4993]

Identify the parent function \(\displaystyle f\)
Describe the sequence of transformations from \(\displaystyle f\) to \(\displaystyle g\)

\(\displaystyle g(x) = -2(x-5)^3+3\)


What does it mean by "the parent function \(\displaystyle f\)" and " the sequence of transformations" ??

The transformations that you are looking for, in general, should be linear (shift -left, right,up & down, contract/expand and reflect).

so the parent function is:

f(x) = x[sup:286pxs3a]3[/sup:286pxs3a]

shift to right 5 spaces ? h(x) = (x - 5)[sup:286pxs3a]3[/sup:286pxs3a]

reflect across(about) x axis ? k(x) = -(x - 5)[sup:286pxs3a]3[/sup:286pxs3a]

Expand twice along y-axis ? m(x) = -2(x - 5)[sup:286pxs3a]3[/sup:286pxs3a]

shift up 3 spaces along y-axis ? g(x) = -2(x - 5)[sup:286pxs3a]3[/sup:286pxs3a] + 3