# Chapter 8 Inverses and Radicals

Document Sample

```					Chapter 8: Inverses and
Lesson 2: Inverses of Relations

Mrs. Parziale
What is a Function?
• A      relation              is a set of ordered
pairs.
•
A function                   is a relation with
ordered pairs whose x-coordinate has only
one      y-coordinate.
• What test can you apply to the graph of a
relation to see if it is a function?
Vertical line test
Function or Not?
• Graph the following relation on
the coordinate grid:
f = { (1,4), ),(2, 8) , ( 3, 8), (0, 0),
(1, -4)}
• Is it a function?
• Create a new function g by
switching the x and y
coordinates of f.
g=
• Is it a function?
• What is the line of symmetry for
f and g?
Inverses
Definition:
The inverse of a relation is the relation obtained by reversing the
order of the x and y coordinates
in each ordered pair in the relation.

• The domain of a relation is the set of all possible values
for the         x                coordinate
• The range of a relation is the set of all possible values of
the        y              coordinate.

• In the examples on the previous slides how do the
domain of f and the range of g compare?
• …the range of f and the domain of g?
Inverse Relation Theorem
Suppose f is a relation and g is the inverse of f. Then:
1) A rule for g can be found by switching        x and y.

2) The graph of g is the reflection image of the graph of f
over the line
y=x

3) The domain of g is the range            of f, and the
range of g is the  domain of f.
Example 1
• Let g = { (4, 3), (0, -1), (5, 2), (-8, -1)}
• a) Is g a function? Why of why not?
• b) Identify the inverse of g.

• c) Is the inverse of g a function? Why or
why not?

The inverse of a relation is always a relation. But the
inverse of a function is not always a function          .
• Graph the function: y = 3x +2
• Complete the chart for coordinates on the graph.

x    (x,y) Inverse of y =3x + 2
(y,x)

0

1

-1

• Graph the inverse of y = 3x + 2
• What is the equation of the inverse of y = 3x +2
• Is the inverse a function?
Theorem ( Horizontal Line Test for
Inverses)
The inverse of a function f is itself a function if and only if
no       horizontal           line intersects the graph of f in
more than one point.

Determine if the inverse of a function is a function. Explain your reasoning.

a)                        b)                  c)
Closure
• How can the inverse of a relation be found
from the coordinates of the relation?
• Explain how the graphs of any relation f an
its inverse are related?
• Give the equation for the inverse of the
relations:
y = 3x – 2          y = 9x2 +12x - 6

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 0 posted: 2/5/2013 language: English pages: 9