N 10-1
Inverses: Graphs of Inverses
A)
B)
C)
D)
E)
F)
Create a table of values in Table 1 for the equation given.
Plot the points from Table 1 on the graph.
Switch the x- and y-coordinates. Record these in Table 2.
Plot the points from Table 2 on the graph.
Draw the line y = x on the graph as a dashed line.
Look for patterns.
1. y = 2x
Table 1
x
y
Table 2
x
y
2. y = -3x + 1
Table 1
Table 2
x
y
x
y
What do you observe?
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N 10-1
When two graphs are reflections of each other over the line y = x, then they
are said to be inverses of each other. This means their “x” and “y”
coordinates have been switched.
3. Find the inverse of the relation.
(4,3),(2,1),(7,0),(1,4),(2,10)
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Graph each of the following functions. Then graph the line y = x as a
dashed line and reflect those points across the line to find the inverse.
Determine if the inverse is a function.
4. 2x – y = 5
**To reflect the points over the
line y = x, all you do is switch
the “x” and “y” coordinates of
the points!! You may use a
table if you’d like.
Is the inverse a Function?________
5. y = x²
Inverse a Function?________
N 10-1
6. y = x³
Table 1
x
y
Table 2
x
y
Inverse a Function?:________
To find the equation of the inverse:
a) Switch x and y in the equation.
b) Re-solve for y.
Notation for an inverse for y is y-1.
For f(x) notation, it is f-1(x).
Write the equation for the inverse of each of the following relations.
7. y = 4x + 8
8. f(x) = 7 – 5x
N 10-1
2
9. y = 2x - 6
Write the equation of the inverse. Graph y = x as a dotted line, and
then graph the following relation and its inverse on the same set of
axes.
10. y = 2x + 4
Is the relation in a function?__________
Is the inverse in a function?__________
11. f(x) = x² + 1
Is the relation a function?__________
Is the inverse a function?___________