If (x, y) lies on the graph of a function, then (y,x) lies on the graph of its inverse.
B
b
To sketch the given function, find the values for a few inputs and draw the line connecting them.
C
c
Inverse functions are found by switching x and y in the equation of the function and solving for y.
D
d
Find corresponding points on the two graphs. Then analyze the relationship between the points.
A
a
See solution.
B
b
C
c
y=2x+6
D
d
Is There a Line of Symmetry? Yes, there is.
Line of Symmetry: y=x
Practice makes perfect
a
Any point on the graph of the function has a corresponding point on its inverse where the x- and y-values are swapped.
b
We are given the following function.
y=1/2x-3We want to graph this function and its inverse. Let's first graph the function. To do so, make a table of values for this function and plot the obtained points.
x
1/2x-3
y=1/2x-3
-4
1/2( -4)-3
-5
-2
1/2( -2)-3
-4
0
1/2( 0)-3
-3
2
1/2( 2)-3
-2
4
1/2( 4)-3
-1
6
1/2( 6)-3
0
Let's plot these point on the coordinate grid and connect them with a smooth line.
Now, recall that to make a table of values of the inverse function we just need to swap the x- and y-coordinates from the table of values of the function.
Function
Inverse
( -4, -5)
( -5, -4)
( -2, -4)
( -4, -3)
( 0, -3)
( -3, 0)
( 2, -2)
( -2, 2)
( 4, -1)
( -1, 4)
( 6, -2)
( -2, 6)
Let's now use the same coordinate grid to plot the inverse using these points.
