Unit 3 Functions

4.1 What is a function?

What is a function? Relation in which each element of the domain (x) is paired with exactly one element from the range [f(x)].

What is a function? For every x there is only exactly one y X can’t repeat

How do we express functions Verbally Last summer I made $10.00 per hour.

How do we express functions Numerically Table/t-chart Time (hours) Pay (dollars) 5 50.00 12 120.00 25 250.00 30 300.00 40 400.00

How do we express functions Algebraically p = 10h

How do we express functions Graphically Pay ($) Time (hours)

Domain Independent variable X variable Input of the function

Range Dependent variable y variable Output of the function

Evaluating a function: A function has a value for every value in its domain “x” represents the domain (input) F(x) represents the range (output) Function notation: f(x) g(x) h(x)

Functional Notation: f(x), g(x), h(x) … g(x) = -x2 + 4x + 1 g(2) 5 g(-3) -20 g(t) -t2 + 4t + 1 g(x + 2) -(x + 2)2 + 4(x+2) + 1 -(x2 + 4x + 4) + 4x + 8 +1 -x2 - 4x - 4 + 4x + 8 +1 -x2 +5

Functional Notation cont: 11/4 f(0) Undefined f(x + 1)

Piecewise Functions f(7) f(-2) f(-5) f(1)

Determine the domain of a function

Find the domain: S: {(-3,0),(-1,4),(0,2),(2,2),(4,-1)} g(x) = -3x2 +4x +5 x   (true for all polynomials) {x  | x ≠ -5} {x  | x ≥ 3} {r  | r > 0} {r  | r ≠ 1, -.5}

Classwork Section 4.1 Pg 217-218: #14-26 even #36-46 even, 55, 59, 61