Algebra 2 – NOTES: Function Notation Day 1
Name_____________________________________________ Date: _________________
Key concepts to review:
 Integer operations
o Adding, subtracting, multiplying, dividing any number including negatives
 Order of operations
 Evaluating/Function Notation
o The use of parentheses
ORDER OF OPERATIONS – The rules of which calculation comes first in an expression
Parentheses
Exponents
Multiplication and Division
Addition and Subtraction
INTEGER - Whole numbers and their opposites (think of the number line):
…-3, -2, -1, 0, 1, 2, 3
ABSOLUTE VALUE – A number’s distance from 0 on a number line.
a) 3 =
b) -4 =
Things to note:
1. Distance is always positive
2. Absolute value is a grouping symbol just like parentheses; So always simplify inside completely,
then take the absolute value of that number.
c) -25+15 =
d) -25 + 15 =
Adding Integers
 Same Signs – add the two numbers and keep the sign (positive/negative)
a) 2 + 5 =

( ) ( )
b) -2 + -5 =
Different Signs – subtract the smaller number from the larger number and keep the sign of the larger
number
a) -2 +5 =
( )
b) 2 + -5 =
Subtracting Integers
 Change the minus sign to “add the opposite” and use the rules for addition above
a) 3-8 =
b) -3-8 =
( )
c) 3- -8 =
( )
d) -3- -8 =
Multiplying and Dividing Integers
 The product or quotient of two positive numbers is POSITIVE
 The product or quotient of two negative numbers is POSITIVE
 The product or quotient of one positive number and one negative number is NEGATIVE
( )
b) -2 ¸ -2 =
a) 2× 2 =
c) -2× 2 =
Evaluating – BE SURE TO USE PARENTHESES!!!!
If x = -4, y = 3, and z = -2 evaluate the following:
a) 2 y - z
b) x - y - z 2
FUNCTION:
 A relationship between input and output
 Each element of the domain is paired with exactly one element of the range.
o In other words, there is exactly one output for each input.
o The x-values can’t repeat and give you two different answers for y.
 On a graph, it passes the vertical line test
Function Notation:
You use the symbol f(x) in place of y. You read f(x) as “f of x”. It does not mean f times x.
For example, consider y = 3x -8
EQUATION:
y = 3x -8
FUNCTION:
f (x) = 3x -8
Suppose you want to find the value in the output that corresponds to the input 5. In other words, you want to
evaluate the function if x equals 5. This is written as f(5) and is read as “f of 5.” The value f(5) is found by
substitution 5 for x into the equation.
f (x) = 3x - 8
f (5) = 3(5) - 8
= 15 - 8
=7
Examples:
Evaluate the following examples that are in function notation. Be sure to follow order of operations and
show your work.
1. Given f (x)  4x  7, evaluate f (2)
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2. Given g(x)  x 2  4 x , evaluate g(1)
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3. Given f (x)  6x 7 and g(x)  3  x 2 , evaluate the following:
a) f (3)
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b) g(3)
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c) A look ahead:
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f (2)  g(0)
Algebra 1
Name_____________________________________________ Date: _________________
HOMEWORK – Function Notation Sheet 1
For #1-6: Given f (x)  2x  4 and g(x)  x  3 find each value. You must show all work!
1.
2. g(2)
f (4)
3.
f (5)
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4. g(3)
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1
6. f ( )
4
5. f (0)
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For #7-12: Given f (x)  3x  2 and g(x)  x 2  x find each value. You must show all work!
7.
8. g(3)
f (4)
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10. g(2)
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f (2)
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9.
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11.
1
f ( )
3
12. g(0.5)
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TURN OVER TO FINISH
#13. Given f (x) 
x 3
evaluate f (7) .
2 ,
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#14. Given h(x)  2  x , evaluate h(5) .
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#15. Given g(x)  8  x , evaluate g(4) .
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#16. Given h(x)  2x  x  3 , evaluate h(1) .
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Review order of operations – Simplify the following:
#17.
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25  8  3
4  3
#18. 3(2)2 (1)  (3)(2)
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