Graph with f(x)

Date: 10/17/2001 at 11:17:47
From: angela Salerno
Subject: Sketching the graph with f(x) in it

Dear Dr. Math,

I am told to sketch the following equations, but do not know how to:

   y = f(x)+ 2

   y = f(x-3)

   y = 2f(x)

Thank you for helping me.
Angela

Date: 10/17/2001 at 12:21:14
From: Doctor Peterson
Subject: Re: Sketching the graph with f(x) in it

Hi, Angela.

Were you told what f(x) is? Without that, you can't really sketch the 
graph.

But if you were given just the graph of f(x), say some random squiggly 
line, you can graph these by seeing how they are related to f(x).

    |       __
    |      /  \f(x)
    |  ___/    \
    | /         \___
    |/
    +---------------


g(x) = f(x)+2 is 2 units higher than f(x) for any x; so you just shift 
the graph upward 2 units:
            __
    |      /  \f(x)+2
    |  ___/    \
    | /     __  \___
    |/     /  \f(x)   ^
    |  ___/    \      | 2 units
    | /         \___  v
    |/
    +---------------


h(x) = f(x-3) has the same value for a given value of x that f(x) has 
when x is 3 less. That is, the graph is shifted to the right three 
units, so that for example h(3) = f(3-3) = f(0).

    |       3 units
    |       <----->
    |       __     __
    |  f(x)/  \   /  \f(x-3)
    |  ___/   _\_/    \
    | /      /  \___   \___
    |/      /
    +---------------


k(x) = 2f(x) is twice as high as f(x) at any given value of x; so you 
are stretching the graph vertically:
            __
    |
    |      /  \2f(x)
    |
    |  ___/    \
    |       __
    | /    /  \ \___
    |  ___/    \
    |//     f(x)\___
    |/
    +---------------

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/