Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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http://lps.lexingtonma.org/Page/2434
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Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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http://lps.lexingtonma.org/Page/2434
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Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Function Notation
Name:
Date:
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Example:
Use the following four functions. There may be more than one answer for each part.
! ! ! !" ! !!!!!!!!!!!! ! ! ! ! ! !!!!!!!!!!!!!!!! ! ! !!! ! ! ! !!!!!!!!!!! ! ! !! ! !
For which function or functions will an input of 5 give an output of 21?
! ! ! !" ! ! !
! ! ! !" ! !"
! ! ! !"
! ! ! !!!! ! !
! ! ! !" ! !
! ! ! !"
! ! !! !!!
! ! ! ! !"
! ! ! !"
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! ! ! !" ! !
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Both h(5) and k(5) equal 21, which means each of these two functions gives an
output of 21 for an input of 5.
Which function results in this input-output table?
g(0)=10
h(0)=-4
j(0) = 25
k(0) = -4
Input
0
1
Output
25
30
Because only j(x) matches for an input of 0, I only have to try an input of 1 in j(x).
j(1) = 5(1+5) = 5(6) = 30, so this table must be from j(x).
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Name:
Date:
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Input
1
2
Output
14
18
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Use the functions ! ! ! !! ! !!!!!!! ! ! ! !!!!!!! ! ! !!!. Evaluate each expression.
Example: ! !
Plug 3 in for ! in the ! ! expression. Use parentheses. Then simplify the expression.
! ! !! ! !!
! ! !!!!
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3. Use the functions below. Evaluate each expression. Be sure to simplify your answer fully.
! ! ! !! ! !!!!!!!! ! !
a. ! !
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b. Find ! !
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Name:
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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This is not a function because for the
input of 2, you could add 2 and get 4 or
add 3 and get 5. Because an input of 2
has more than one output, this is not a
description of a function.
!
Name:
Date:
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This is a function because each person
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each input has only one output.
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
!
Domain (allowable x-values) and Domain Restrictions:
Name:
Date:
The four basic functions (below) and variations of them have a domain of All Real Numbers
! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! ! ! !!!!!!!!!!!!!!!!!!!! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! !!!
Rational functions: The denominator cannot equal zero. Write the denominator is not equal to
0. Solve as if it were an equation.
Example:
!
! ! ! !!!!
!! ! ! ! !
!! ! !
!
!! ! !
(Add three to both sides)
(Divide both sides by 2)
!
The domain of g(x) is all Real numbers except ! ! !
Radical functions: The number under the square root cannot be negative. Write the expressions
under the square root sign is ! !. Solve the inequality.
Example:
! ! ! !!!
! ! ! ! ! (Subtract three from both sides.)
! ! !!
The domain of f(x) is all Real numbers where ! ! !!
You Try:
5. Determine the domain of each function.
a. ! ! ! ! ! !
!
!
b. ! ! ! !!!!
c. ! ! ! !! ! !
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
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This graph does show a function because
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Math 1: Algebra, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
!
Domain and Range of Tables!
The domain is the set of all inputs. The range is the set of all outputs. A table represents a
function if no input has more than one output.
Example: Find the Domain and Range of the table. Then determine if the table represents a
function.
Input
0
2
-3
4
2
Output
2
3
2
6
-2
Domain: !! !! !!! !! !
Range: !!! !! !! !
The table does not represent a function because the
input of 2 has more than one output (3 and !2)
!
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7. Find the domain and range of the relation represented by the input-output table below. Then
determine if the table represents a function.
Input
0
2
-3
4
5
Output
2
3
2
6
-2
Domain:
Range:
!
!
Is it a Function (explain):
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Q9!#(,A!-'3!A$E0(,!$*!-'3!1%0<'9!
6
4
4
2
2
–5
5
–2
!
!
The domain of the graph is all Real number xvalues greater than or equal to !2.
–4
–5
5
–2
–4
!
Domain: all !! ! !!2!
!
!
P!