Graphing (Precalculus) Homework: Transforming Functions for y=(x-3)^2 and y=x^n

[frozenbananas]

Homework Statement

Sketch the graph of the function y=(x-3)^2 by transforming the graph of an appropriate function of the form y=x^n

Homework Equations

y=(x-3)^2, y=x^n

The Attempt at a Solution

Precisely speaking, I am just totally confused with what the question is asking. i mean i know how to graph y=(x-3)^2 bit idk what the y=x^n is about. thanks so much!

 

[CompuChip]

If you look carefully at the exponents, you might guess that they mean n = 2.
So the question is, through what (geometric) operation(s) can you obtain the graph of (x - 3)³ from that of x²?

Since x² is a basic graph (you should be able to draw it by heart), given this set of operations you can also draw (x - 3)².

 

[HallsofIvy]

Generally speaking, anything that is done to x before the "basic function" is a change in x and so changes the graph horizontally. Anything that is done after the "basic function" is a change in y and so changes the graph vertically.

Here, the "basic function" is $x^2$ and $(x- 3)^2$ is just $x^2$ with 3 subtracted from x before the square. The graph of $y= x^2$ itself is a parabola with vertex at (0, 0). x- 3= 0 when x= 3. The graph of $y= (x- 3)^2$ is the graph of [itex]y= x^2[/tex] shifted three places to the right- a parabola with vertex at (3, 0).[/itex]