Download 2.2.1 * Linear Functions

2.2.1 – Linear Functions
• There are several types of functions we will
deal with throughout the year
• First type is known as linear
• Linear = a function that may be written as the
form y = mx + b
– Highest power of x is “1”
– No x in denominators
– No other variables present
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Examples of linear functions:
f(x) = 3x + 5
f(x) = -2x – 4
f(x) = x
f(x) = x + 2
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Examples of non-linear:
f(x) = x/(x+1)
f(x) = x2 + 2
f(x) = x3/2
• Example. Tell whether the following functions are
linear or non-linear:
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A) f(x) = 2x + 4
B) f(x) = 2x2 + 4
C) f(x) = 4/x
D) f(x) = 1 – 16x
E) f(x) = 4
F) f(x) = -x - 2
Function Notation
• With functions, we won’t always use the
expression y = …. or x = …
• Remember, could have multiple letters; must be
able to determine what the actual variable is
• Function notation does 2 things
– 1) Gives a name to the function (typically a single
letter)
– 2) Tells us what the actual variable is (everything else
then, is a constant)
Function Notation
• Function notation will always be written in the
form;
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f(x) = …
a(y) = …
g(z) = …
f(y) = ….
• The part before the parenthesis is the function
name
• The portion inside the parenthesis is the variable
of interest (IE, the number you plug numbers in
for, solve for, use frequently)
• Example. Given the function f(x) = 3x + 1,
evaluate f(2).
• When dealing with functions names and
values, always look inside the parenthesis
– What is the value?
– What is the variable we need to substitute for?
• Example. Given g(x) = 4x – 5, evaluate g(-3).
– Variable?
– Value?
– Substitution?
• Example. Evaluate the following functions for
f(3).
• A) f(x) = 3x – 1
• B) f(x) = x3 + 2
• C) f(x) = 3
• With a partner, come up with:
• 2 examples of linear functions
• 2 example of non-linear functions
• Write in function notation for evaluating a
function (IE, f(2))
• Pass along to a different set of partners,
reconvene
• Assignment
• Pg. 76
• 1-8, 14-26 even