Grade 12 Pre-Calculus Mathematics [MPC40S] Chapter 10
Transcript of Grade 12 Pre-Calculus Mathematics [MPC40S] Chapter 10
Grade 12 Pre-Calculus Mathematics
[MPC40S]
Chapter 10
Function Operations
Outcome
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12P.R.1. Demonstrate an understanding of operations on, and compositions of, functions.
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Chapter 10 β Homework
Section Page Questions
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Chapter 10: FUNCTION OPERATIONS
10.1 β Sums and Differences of Functions
We can form new functions by performing operations with functions. To combine two functions, π(π₯) and π(π₯), add or subtract as follows: Sum of Functions Difference of Functions π(π₯) + π(π₯) π(π₯) β π(π₯) (π + π)(π₯) (π β π)(π₯) Example 1
Given π(π₯) = π₯ + 1 and π(π₯) = 2π₯ β 3. a) Write an equation to represent π(π₯) + π(π₯) Domain:____________________ b) Write an equation to represent π(π₯) β π(π₯)
Domain:______________________
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Example 2
a) Given the graphs of π(π₯) = π₯2 and π(π₯) = β2π₯ + 1 below sketch (π + π)(π₯)
b) Write an equation to represent (π + π)(π₯)
π₯ π(π₯) π(π₯) π(π₯) + π(π₯)
β2
β1
0
1
2
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Example 3
Given the graphs of π(π₯) and π(π₯). Sketch the graph of (π β π)(π₯) Domain:_________________________________
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Example 4
Use the following graphs to sketch the graph of π(π₯).
)(xf ( )( )xgf β
π₯ π(π₯) π(π₯) (π β π)(π₯)
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Chapter 10: FUNCTION OPERATIONS
10.2 β Products and Quotients of Functions
We can form new function by performing operations with functions. To combine two functions, π(π₯) and π(π₯), multiply or divide as follows: Product of Functions Quotient of Functions
π(π₯)π(π₯) π(π₯)
π(π₯)
π β π)(π₯) (π
π) (π₯)
Example 1
Given the functions π(π₯) = π₯ + 1 and π(π₯) = 2π₯ β 3
a) Write an equation for π(π₯) β π(π₯) Domain:_________________________
b) Write an equation for π(π₯)
π(π₯)
Domain:__________________________
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Example 2
Using the graphs of π(π₯) and π(π₯) given below, answer the following questions:
a) Identify the zeros of (π β π)(π₯). b) State the vertical asymptote(s) of
(π
π) (π₯)
c) Evaluate the following expressions
a) (π
π) (1) b) (π β π)(β3) c) (
π
π) (0)
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Chapter 10: FUNCTION OPERATIONS
10.3 - Composite Functions
Composite Functions:
- Are functions that are formed from two functions, π(π₯) and π(π₯) , in which the output (or result) of one of the functions is used as the input for the other function.
- The composition of π(π₯) and π(π₯) is defined as ______________ and is formed
when the equation of π(π₯) is substituted into the equation of π(π₯).
- ______________ is read as _____________________________.
- We can write composite function as _______________ or _______________.
- Composite functions must not be confused with multiplication. That is (π β π)(π₯) is not the same as (π β π)(π₯).
Example 1
Given π(π₯) = π₯2 + 1 and π(π₯) = 2π₯ β 3
a) Determine the equation for π(π(π₯))
b) Determine the equation for (π β π)(π₯)
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c) Determine the equation for π(π(π₯)) d) Evaluate π(π(2))
e) Evaluate (π β π)(1)
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Example 2
Use the table below to evaluate the following.
x 1 2 3 4 5 6
π(π₯) 3 1 4 2 2 5
π(π₯) 6 3 2 1 2 3
a) π(π(2)) b) π(π(0))
c) (π β π)(3)
d) (π β π)(1)
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Example 3
Given π(π₯) = 2π₯ β 3 and π(π₯) =π₯+3
2, determine π(π(π₯)) and π(π(π₯)).
π(π(π₯)) π(π(π₯))
Recall: When π(π(π₯)) = π₯ or π(π(π₯)) = π₯, this means that π(π₯) and π(π₯) are
__________________ of each other.
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Example 4
Use the graphs below to answer the following questions:
a) π(π(2)) b) π(π(4))
c) Determine the value of x if f(g(x)) = 3.
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Example 5
Given π(π₯) = βπ₯ + 3 and π(π₯) = π₯2 β 4. a) Domain of π(π₯) _____________ Domain of π(π₯) ________________
b) Determine π(π(π₯)) and identify the domain.
c) Determine π(π(π₯)) and identify the domain.
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d) Graph π(π(π₯)).
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CHAPTER 10 REVIEW: Old Exam Questions Outcome R1
June 2015
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January 2015
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June 2014
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January 2014
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June 2013
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January 2013
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