Unit 1: Functions Minds On What do you think of when you hear “inverse”?
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Unit 1: Functions Minds On What do you think of when you hear “inverse”?
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Transcript of Unit 1: Functions Minds On What do you think of when you hear “inverse”?
Unit 1: Functions
Minds On
What do you think of when you hear “inverse”?
Unit 1: Functions
Minds On
a) Graph: f(x) = (x – 2)2 - 1 and determine the domain and range
b) Graph the inverse by switching all the (x, y) coordinates. Determine the domain and range of the inverse.
Unit 1: Functions
Lesson 5: Inverse Functions
Learning Goal:
I can determine the inverse of a function and its algebraic expression, set of values (ordered pairs) as it relates to the original function.
Unit 1: Functions
Lesson 5: Inverse Functions
Unit 1: Functions
Lesson 5: Inverse Functions
Properties of the Inverse of a Function •If (a, b) is a point on the graph of y = f(x), then (b, a) is a point on the graph of y = f-
1(x)
•The domain of f(x) will be the range of f-1(x)
•The range of f(x) will be the domain of f-1(x)
•The graph of y = f-1(x) is the reflection of y = f(x) in the line y = x
Unit 1: Functions
Lesson 5: Inverse Functions
Unit 1: Functions
Lesson 5: Inverse Functions
i. graph the relationship and state domain and range D= R =
Given the relation {(-2,3), (0,4), (2,5), (3,4), (5,2), (6,l)}
ii. switch the x and y coordinates to graph the inverse relationship and state the domain and range
D= R =
iii. Graph the line y = x. Compare the points on the original function and their corresponding points on the inverse. What do you notice?
Unit 1: Functions
Lesson 5: Inverse Functions
How do we determine the inverse of a function? 1) Replace f(x) with y
f(x) = 3x - 5 becomes y = 3x - 5 2) Switch x and y in the equation.
y = 3x - 5 becomes x = 3y - 5
Unit 1: Functions
Lesson 5: Inverse Functions
Unit 1: Functions
Lesson 5: Inverse Functions
Example: Find the inverse of f(x) = x + 2
Unit 1: Functions
Lesson 5: Inverse Functions
Example: Find the inverse of f(x) = 2x
Unit 1: Functions
Lesson 5: Inverse Functions
Unit 1: Functions
Lesson 5: Inverse Functions
Given the function h(x) = 2x – 4, determine h-1(-3)
Unit 1: Functions
Lesson 5: Inverse Functions
Example: Find the inverse of f(x) = (x – 3)2 + 5
Unit 1: Functions
Lesson 5: Inverse Functions
The inverse of a quadratic is NOT a function.We can make it a function by restricting the domain.
Unit 1: Functions
Lesson 5: Inverse Functions
NEW Homework
Pg. 46-49 #1a, 2bd, 4, 6, 8, 9a-e, 10ace, 15
Pg. 160-162 #1a, 2b, 3, 4, 10
Extra: Level 4 Pg. 46-49 #16, 17
Pg. 160-162 #13
