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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 • • • • • Examples of linear functions: f(x) = 3x + 5 f(x) = -2x – 4 f(x) = x f(x) = x + 2 • • • • 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: • • • • • • 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; – – – – 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