Help creating tables from graph

[crazydaizy78]

:shock: My cat could probably do better than I at this class!!

#3: Graph each of the transformations of (f)or (g) and find the formula for the transformed function.
Find: y=g(-2x)

I'm given from the graph: f(x) is x^2 & g(x) is x^3. From there in input the given info into calc but g(x) comes out looking nothing at all like the original graph. Not sure why.

So I moved on, and created a table for x & g(x) by using the visual points on the graph, and added a column for -2x. Now I'm lost as to how to show the column for g(-2x).

Teacher has given me the answer, but I want to figure it out and know it. No need to take the class if I don't learn. Let me know if you'd like me to scan in my work thus far &/or the teachers answer. Below is the list of pts:
x g(x) -2x
-6 -3.75 12
-4 -3 8
-2 -2.5 4
0 0 0
2 2.5 -4
4 3 -8
6 3.75 -12

 

[jwpaine]

For \(\displaystyle g(x) = x^{3},\,\,\,\,g(-2x) = (-2x)^{3}\)

Now
\(\displaystyle y = g(-2x) = (-2x)^{3}\)

input for x
\(\displaystyle x =\,\,\, [-6,\,\,\,-4,\,\,\,-2]\)

output of g(x)
\(\displaystyle g(x) =\,\,\, [ (-6)^3,\,\,\,(-4)^3,\,\,\,(-2)^3 ]\)

output of g(-2x)
\(\displaystyle g(-2x) =\,\,\, [ -2(-6)^3,\,\,\,-2(-4)^3,\,\,\,-2(-2)^3]\)

As you can see, we have a non-rigid transformation: you should be able to plot the points for x, g(x) and then for x, g(-2x) and see the transformation. You should plot more than three points, the above is an example.....hope this helps!

John

 

[crazydaizy78]

You're my hero!! Amazing how simple the answer is yet how hard I made it for meyself to find. Thanks a bunch!