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Transcript 
Lesson 12-1
Inverse Relations & Functions
Objectives
Students will:
•Write inverse equations from a given equation
•Determine symmetry about the line y = x
•Find equations for inverse functions
Graph the equation y1 = 2x – 4
List some order pairs from quadrant 1
(2, 0), (3, 2), (4, 4)
Now graph y2  1 x  2
2
List some ordered pairs from quadrant 1
(0, 2), (2, 3), (4, 4)
Ordered pairs are:
y2
switched: (x, y) → (y, x)
Graphs are:
Reflected over line y = x
Equations are:
Inverses → switch y & x in one equation,
solve for y and you get the other
y1
Inverse Relations & Functions
Equation
Switch x & y value
Solve for new y value
Give new name for inverse: y’ or f-1(x)
Symmetric if y’ or f -1(x) is same as original
Graph
Switch x & y values
Reflected over y = x
Symmetric if graphs are the same
Example 1 Find the inverse, f -1(x), of y = 3x + 2
Example 2 Is x2 + 3x2y2 + y2 = 1 symmetric?
HW 114
Ch 11 Notes Quiz
Tomorrow
Graph the equation y1 = 2x – 4
List some order pairs from quadrant 1
y2  1 x  2
2
List some ordered pairs from quadrant 1
Now graph
Ordered pairs are:
Graphs are:
Equations are:
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