1 7 FUNCTIONS OBJECTIVES Determine whether a relation
1. 7 FUNCTIONS
OBJECTIVES • Determine whether a relation is a function. • Evaluate functions.
What is a Function? Input (x) DOMAIN Output (y) RANGE A function is a rule that establishes a relationship with an input and an output.
What is a Function? Input (x) DOMAIN Output (y) RANGE function – a relation where each input matches up with exactly one output
(1, -1) Relation – a pairing of input and output numbers
f x y (inputs) (outputs) 1 -1 2 0 3 1 5 3 8 6 relation – a pairing of input (domain) and output (range) numbers
domain f x y (inputs) (outputs) 1 -1 2 0 3 1 5 3 8 6 relation – a pairing of input (domain) and output (range) numbers * A set of ordered pairs
domain f range x y (inputs) (outputs) 1 -1 2 0 3 1 5 3 8 6 relation – a pairing of input (domain) and output (range) numbers Domain = D {1, 2, 3, 5, 8} Range = R {-1, 0, 1, 3, 6} independent
What is a Function? Input (x) DOMAIN Output (y) RANGE function – a relation where each input matches up with exactly one output
x f (x) -1 3 0 3 1 3 3 3 6 3 3 3 Is f (x) a function? YES! function – a relation where each input matches up with exactly one output If an input value is put in multiple times, you will get the same output every time.
x f (x) Is f (x) a function? NO! 1 3 0 13 WHY? Check yourself! 1 -3 4 3 • Does each input match up with exactly one output? 6 5 3 1 • If an input value is put in multiple times, do you get the same output every time?
Identify a Function Which relation is not a function? x y x y -1 -1 1 11 1 9 0 0 2 21 5 15 1 1 3 31 -2 -6 3 3 3 41 3 9 6 6 4 51 7 15
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How can I tell if it’s a function? REAL WORLD EXAMPLES
How can I tell if it’s a function? REAL WORLD EXAMPLES l People vs. Places
Relation: Different Form {(1, -1), (2, 0), (3, 1), (5, 6), (8, 6)} Is this relation a function? Hint: Look at all of the input values first!
Relation: Different Form {(1, -1), (2, 0), (3, 1), (5, 6), (2, 4)} Is this relation a function?
f x y (inputs) (outputs) -6 -9 Find: -5 -7 1. domain -1 3 2. range 2 4 6 7 3 -7 3. y if x = -1 4. x if y = 7
f x y (inputs) (outputs) -6 -9 -5 -7 -1 3 2 4 6 7 function notation For function f: y=3 f (-1) = 3 “The value at x = -1 is 3. ”
Graph it! x f (x) 1 3 0 13 1 -3 4 3 6 5 3 1 Is f (x) a function? NO! Vertical Line Test – as a vertical line passes it never touches more than one point on the graph
Graph it! g(x) = -3 x – 6 Is g(x) a function? YES! f (x) = mx + b linear function
Is this a graph of a function? NOT A FUNCTION!
Is this a graph of a function? FUNCTION!
Evaluating Functions Remember f(x) is just function notation! A. If f(x) = 3 x – 4, find f (4). 4. f(4) = = 3(4) – 4 Replace x with 12 – 4 Multiply. = 8 Subtract. Answer: f(4) = 8
B. If f(x) = 3 x – 4, find f(– 5).
A. If h(t) = 1248 – 160 t + 16 t 2, find h(3).
CHALLENGE!!! The function h(t) = 180 – 16 t 2 represents the height of a ball thrown from a cliff that is 180 feet above the ground. A. Find h(2 z).
Algebra A/B Homework: 1. 7 Practice Worksheet (ODDS)
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