7.7 inverse relations and functions - weebly
TRANSCRIPT
Using a graphing calculator, graph the
pairs of equations on the same graph.
Sketch your results. Be sure to use the
negative sign, not the subtraction key.
82
)8(2/1
xy
xy
3
3
32
xy
xy
xy
2
2
22
xy
xy
xy
What do you notice
about the graphs?
These graphs are
said to be inverses
of each other.
An inverse relation “undoes” the
relation and switches the x and
y coordinates.
In other words, if the relation has
coordinates (a, b), the inverse has
coordinates of (b,a)
X Y
0 3
1 4
-3 0
-5 2
2 5
-8 5
X Y
3 0
4 1
0 -3
2 -5
5 2
5 -8
Function f(x) Inverse of
Function f(x)
Let’s look at our graphs from earlier.
Notice that the points of the graphs are
reflected across a specific line.
82
)8(2/1
xy
xy
3
3
32
xy
xy
xy
2
2
22
xy
xy
xy
What is the equation of
the line of reflection?y = x
Finding the Inverse of an
equation
yx 3
Find the inverse of
y=x2+3
x=y2+3
x – 3 = y2
Switch the x and y
Solve for y
Find the square root
of both sides
What happens if I don’t
include the + ?
Graphing the
function and only the
positive graph of the
inverse . . . We only get
half of the
inverse graph.
Finding the Inverse of a
function
2 xxf
22 yx
22 )2( yx
Rewrite using y
Switch the x and y
Square both sides
Solve for y
When we find the inverse of a
function f(x) we write it as f-1
22 xy
2 xy
2 yx
Find the inverse of