Addition - Mr. T's Classes 6/L6.2/Slides.pdf · 13 Finding the DOMAIN of a function L6.2 The DOMAIN...
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1 Addition f(x) =3x g(x) = x 5 Function Operations L6.2 f(x) + g(x) = (3x) + (x 5) = 3x + x 5 = 4x 5 h(x)= Create a new function by adding 2 other functions together
Transcript of Addition - Mr. T's Classes 6/L6.2/Slides.pdf · 13 Finding the DOMAIN of a function L6.2 The DOMAIN...
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Addition
f(x) = 3x g(x) = x 5
Function Operations L6.2
f(x) + g(x) = (3x) + (x 5)
= 3x + x 5
= 4x 5
h(x) =
Create a new function byadding 2 other functions together
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Subtraction
f(x) = 3x g(x) = x 5
Function Operations L6.2
f(x) g(x) = (3x) (x 5)
= 3x x + 5
= 2x + 5
h(x) =
Create a new function bysubtracting 2 other functions
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Function Operations L6.2
Multiplication
f(x) = 3x g(x) = x 5
f(x) * g(x) = (3x)(x 5)
= 3x*x 3x*5
= 3x2 15x
h(x) =
Create a new function bymultiplying 2 functions
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Function Operations L6.2
Division
f(x) = 3x g(x) = x 5
f(x) ÷ g(x) = g(x)f(x)
= x 53xh(x) =
Create a new function bydividing 2 other functions
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Function Operations L6.2
f(x) = x + 3 g(x) = 2x 1
f(x) + g(x)h(x) = =
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f(x) g(x)h(x) =
Function Operations L6.2
f(x) = x + 3 g(x) = 2x 1
=
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f(x) * g(x)h(x) =
Function Operations L6.2
f(x) = x + 3 g(x) = 2x 1
=
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f(x) ÷ g(x) = h(x) =
Function Operations L6.2
f(x) = x + 3 g(x) = 2x 1
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3f(x)h(x) =
Function Operations L6.2
f(x) = x + 3 g(x) = 2x 1
=
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2f(x) + g(x)h(x) =
Function Operations L6.2
f(x) = x + 3 g(x) = 2x 1
Do # 1320Pg 294
=
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f(x) g(x)
x + 32x 1
= 3x + 2
= x + 4
= 2x2 + 5x 3
= 4x + 5
= 3x + 9
= x + 3 2x + 1
Function Operations L6.2
f(x) = x + 3 g(x) = 2x 1
f(x) + g(x)
f(x) * g(x)
f(x) ÷ g(x)
3f(x)
2f(x) + g(x)⇒
(x + 3)(2x 1) = 2x2 x + 6x 3
=
3(x + 3)
= 2x + 6 + 2x 1
(x + 3) + (2x 1) = x + 3 + 2x 1
(x + 3) (2x 1)
2(x + 3) + (2x 1)
⇒
⇒
⇒
⇒
Do # 1320Pg 294
h(x) =
h(x) =
h(x) =
h(x) =
h(x) =
h(x) =
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14) h(x) = x + 1
16) h(x) = 2x + 1
18) h(x) = 2x2 + 2x
20) h(x) = x + 12x
Function Operations L6.2
Do # 1320Pg 294
13) h(x) = 3x + 1
15) h(x) = 2
17) h(x) = 2x2 + 2x
19) h(x) = x + 12x
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Finding the DOMAIN of a function L6.2
The DOMAIN is all the x's that can be used for the function...
ASK: are there any x's that can't be used with the function?
• What are some things you simply can't do with numbers?
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= ? √3 = ?
Can't divide by zero Can't take square root of a negative
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Domain is all real numbersexcept where have:
• ÷ by zero• √ of a negative
nono
Finding the DOMAIN of a function L6.2
What is the DOMAIN of:
f(x) = 7x + 19
• Check for divide by zero
...no fractions so no division by zero possible
Domain is all real numbers
• Check for square root of a negative
...no square root so square root of a negative possible
all R
look for variable in den
ominator...
look for variable in √...
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Finding the DOMAIN of a function L6.2
What is the DOMAIN of:
f(x) =
• Check for divide by zero
...has a fraction!
• Check for square root of a negative
...no square root so square root of a negative possible
2x + 5x 3
...when would we have a zero in the denominator?
...when x 3 = 0
Domain is all real numbersexcept where have:
• ÷ by zero• √ of a negative no
if x = 3
all R except 3
or when x = 3
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Finding the DOMAIN of a function L6.2
What is the DOMAIN of:
f(x) =
• Check for divide by zero
...doesn't have a fraction...no division by zero worries
• Check for square root of a negative
...has a square root...when would we have a negative inside?
√2x + 4
...when 2x + 4 < 0 4 42x < 4x < 2
Domain is all real numbersexcept where have:
• ÷ by zero• √ of a negative
noif x < 2
Do # 5 12
Pg 294domain only...
all R ≥ 2
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Finding the DOMAIN of a function L6.2
5) all R6) all R7) all R8) all R9) all R ≥ 3
10) all R ≥ 1
11) all R except 1
12) all R except 3
Domain is all real numbersexcept where have:
• ÷ by zero• √ of a negative
noif x < 2
Do # 5 12
Pg 294domain only...
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f( g(x) ) = 2(x 3) + 1
g(x) g(x)
Putting a function in a function? L6.2
The composite of functions
pronounced f of g of x
Plug one function into another
f( g(x) )
f(x) = 2x + 1 g(x) = x 3
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g(x) = x 3
f( g(x) ) = 2(x 3) + 1
Putting a function in a function? L6.2
The composite of functions
pronounced f of g of x
Plug one function into another
f( g(x) )
f(x) = 2x + 1
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f( g(x) ) = 2(x 3) + 1
Putting a function in a function? L6.2
The composite of functions
pronounced f of g of x
Plug one function into another
f( g(x) )
f(x) = 2x + 1 g(x) = x 3
= 2*x 2*3 + 1
= 2x 6 + 1= 2x 5
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g( f(x) ) =
Putting a function in a function? L6.2
The composite of functions
pronounced g of f of x
Plug one function into another
g( f(x) )
f(x) = 2x + 1 g(x) = x 3
g(x) = x 3
(2x + 1) 3
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g( f(x) ) =
Putting a function in a function? L6.2
The composite of functions
pronounced g of f of x
Plug one function into another
g( f(x) )
f(x) = 2x + 1 g(x) = x 3
= 2x + 1 3
= 2x 2
g(x) = x 3
(2x + 1) 3
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g( f(x) ) =
Putting a function in a function? L6.2
The composite of functions
pronounced g of f of x
Plug one function into another
g( f(x) )
f(x) = 2x + 1 g(x) = x 3
= 2x + 1 3
= 2x 2
g(x) = x 3
(2x + 1) 3
Do # 2126Pg 294
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Putting a function in a function? L6.2
21) f(g(x)) = 2x + 1
g(f(x)) = 2x + 2
22) f(g(x)) = 2x 5
g(f(x)) = 2x 2
23) f(g(x)) = x2 2x + 1
g(f(x)) = x2 1
Do # 2126Pg 294
24) f(g(x)) = x2 + 4x + 3
g(f(x)) = x2 + 1
25) f(g(x)) = x
g(f(x)) = x
26) f(g(x)) = x2 10x 26
g(f(x)) = x2 + 4
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L6.2 HW Problems
Pg 294, #134, 4455
L6.2
