Grade 12 Pre-Calculus Mathematics Notebook Chapter 10 Function Operations Outcomes: R1
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Grade 12
Pre-Calculus Mathematics Notebook
Chapter 10
Function
Operations
Outcomes: R1
Page 2
Page 3
10.1 Sums and Differences of Functions R1 Pages 472-483 Ex1: Given and . a) Write an equation to represent h(x) if . b) Write an equation to represent k(x) if . c) Sketch the graphs of and on the graph below. Note: To find the new values of k and h, we simply have to perform the
given operation on the y-values of f and g.
1)( += xxf 32)( -= xxg
)()()( xgxfxh +=
)()()( xgxfxk -=
( ), ( ), ( )f x g x h x )(xk
Page 4
Ex2: a) Sketch and . b) Sketch using only the graphs of f and g. Note: We simply need to add the y-values of f and g to do so. c) Write the equation of the function .
2)( xxf = 12)( +-= xxg
( )( )xgf +
( )( )xgf +
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Ex3: Use the following graphs to sketch the graph of .
Often using a table of values is a good strategy to answer these types of problems.
x
)(xg
)(xf ( )( )xgf -
)(xf )(xg ( )( )xgf -
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Note: The domain of the function g must be [–4, 2] since the resulting function only has a domain of [–4, 2].
The domain of a function that is the sum or difference of different functions is made up of the common domains of all the initial functions. Example: Domain of : Domain of : Domain of : Recall: Function Notation If f(x) = x2 – 2 and g(x) = 3x + 1, evaluate:
a) f(5) b) g(f(–3)) Homework: Page 483 #1-4 (choose 2 from each), 5, 6 (choose 2), 7, 9-11(choose 2 each)
( )( )xgf -
)(xf { }2, ³xRx e)(xg { }4, £xRx e
)()( xgxf + { }42, ££ xRx e
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10.2 Products and Quotients of Functions R1 Pages 488-495 Ex1: Given and . a) Write an equation for h(x) if
b) Write an equation for k(x) if
c) Identify the domain of the graphs of h(x) and k(x).
Note: The function in the denominator can never be equation to zero. Therefore, . Ex2: If and , write two possible
solutions for and .
1)( += xxf 32)( -= xxg
)()()( xgxfxh ×=
)()()(xfxgxk =
0)( ¹xf
252)( 2 +-= xxxh )()()( xgxfxh ×=)(xf )(xg
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Ex3: Using the graphs of and given below, answer the following questions:
a) Identify the zeros of the function h(x) if .
Note: When and , the function will also equal zero.
b) Evaluate the following expressions:
Homework: Page 496 #1, 2, 3, 4(a, b), 5(a,b), 6, 7, 8
)(xf )(xg
( ) ))(( xgfxh ×=
0)( =xf 0)( =xg )(xh
( )1÷÷ø
öççè
ægf ( )( )3-× gf ( )0÷÷
ø
öççè
ægf
Page 9
10.3 Composite Functions R1 Pages 499-506
Ex1: Given and . a) Evaluate the composite function . b) Write an equation for . c) Write an equation for . d) Evaluate .
1)( 2 += xxf 32)( -= xxg
( )( )2gf
( )( )xgg
( )( )xfg !
( )( )1-fg !
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Ex2: Use the table below to respond to the following questions.
x 1 2 3 4 5 6 3 1 4 2 2 5
6 3 2 1 2 3
a) b)
c) d)
Ex3: Given and , determine and
. Note: When or , this means that and
are inverses of each other.
)(xf)(xg
( )( )2gf ( )( )0fg
( )( )3fg ! ( )( )1ff !
32)( -= xxf23)( +
=xxg ( )( )xgf
( )( )xfg
( )( ) xxgf = ( )( ) xxfg = )(xf)(xg
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Ex4: Use the graphs below to answer the following questions:
a) b)
c) Determine the value of x if .
( )( )2gf ( )( )4fg
( )( ) 3=xgf
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Ex5: Given and .
a) Determine and identify the domain.
b) Determine and identify the domain.
Note: We must consider the domain of inner function as well as the domain of the composite function.
Homework: Page 507 #1, 2, 3(a & c), 4(a, d, e), 5(a & b), 6–10
3)( += xxf 4)( 2 -= xxg
( )( )xfg
( )( )xgf
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