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pre-calc 1.2&1.3

# pre-calc 1.2&1.3 - Section 1.2 Basics of Functions and...

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Section 1.2 Basics of Functions and Their Graphs A relation is any set of ordered pairs. (ex: ( 29 ( 29 ( 29 ( 29 { } h g f e d c b a , , , , , , , ) - The set of all first components of the ordered pairs is called the domain of the relation. (domain of the example relation = {a, c, e, g} - The set of all second components is called the range of the relation. (range of the example relation = {b, d, f, h}) EX 1: Find the domain and range of the relation: ( 29 ( 29 ( 29 ( 29 ( 29 { } 8 . 21 , 25 , 7 . 20 , 20 , 9 . 18 , 15 , 2 . 16 , 10 , 8 . 12 , 5 Functions A function is a relation in which each member of the domain corresponds to exactly one member of the range. -No two ordered pairs have the same first component with different second components. (note: a function can have two different first components with the same second component) Examples: EX 2: Determine whether each relation is a function. a.) { (1,2), (3,4), (5,6), (5,8) } b.) { (1,2), (3,4), (6,5), (8,5) } Functions as Equations ·Functions are usually given in terms of equations rather than as sets of ordered pairs. ex. y = -0.016x 2 + 0.93x + 8.5 – for each value of x, there is one and only one value of y · x is the independent variable · y is the dependent variable *To determine whether an equation represents a function: Solve for the dependent variable. If you put one value in for the independent value and only get one dependent value, the equation represents a function. EX 3: Solve each equation for y and then determine whether the equation defines y as a function of x: a.) 2x + y = 6

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b.) x 2 + y 2 = 1 Function Notation -- Replace y with f(x); f(x) stands for “function in terms of x” and we say “f of x”.
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pre-calc 1.2&1.3 - Section 1.2 Basics of Functions and...

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