Associated Topics || Dr. Math Home || Search Dr. Math

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/
```
Associated Topics:
High School Equations, Graphs, Translations
High School Functions

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search