Identify the parent function for g from its function rule. Then graph g on your calculator and describe what transformation of the parent function it represents

Question

Identify the parent function for g from its function rule. Then graph g on your calculator and describe what transformation of the parent function it represents.

g(x)=x3+2

 

I need more explaining how will I even know which way to go? I don't have a calculator that creates a graph.. HELP PLEASE

Answer 1

Angie,

The parent function of this is g(x) = x³

For transformations, anything added outside the exponent, as this is, is a move in the y direction as indicated.

Here that means its translates UP 2.

A -2 would mean down 2.

 

Addends inside the exponent, (x + 2)³ is a move in the x direction, opposite what is indicated. So this example means slide LEFT 2.  And (x - 2)³ would mean slide RIGHT 2.

 

Any coefficient on the x indicates a stretch  or shrink of the curve as follows:

 

c>1 means vertical stretch or horizontal shrink (same thing)

0<c<1 means vertical shrink or horizontal stretch (same thing)

c<0 means flipping it across the x axis.

 

I hope this helps. It's hard without a drawing editor. You really should try to get your hands on a graphing calculator. Pawn shops are sometimes a cheaper source.

 

Bryan