Do Now Complete the chart for each linear equation. y = x - 2 4 -3 2 -1 x y 2 -2 1 -1

Advanced Algebra Trigonometry Appendix C Functions Objective: Determine if a relation is a function, and find the domain and range.

Relations Relation: a set of ordered pairs. { ( -3, 2), (-1, 1 ), ( 0, 7), (2, 4), (4, 3)} {( -2, 1), (-1, 2), ( 0, 3), (1, 4), (2, 5)} ( x, y ) Independent Variable Dependent Variable The value of y “depends” on the value of x. Domain: the set of all x-coordinates, independent variable Range: the set of all y-coordinates, dependent variable

Relations Given the relation: State the domain: State the range: {(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)} State the domain: D: {0,1, 2, 3} State the range: R: {-6, 0, 4}

y-values CAN be repeated. Functions Function: a relation in which, for each value of the first component of the ordered pairs, there is exactly one value of the second component. A function is a relation in which the members of the domain (x-values) DO NOT repeat. So, for every x-value there is only one y-value that corresponds to it. y-values CAN be repeated.

Ways to Represent a Function Symbolic Graphical X Y 1 2 5 10 -1 -2 3 6 Numeric Verbal The cost is twice the original amount.

Does the relation represent a function? No, 3 is repeated in the domain. G = {(4, 1), (5, 2), (8, 2), (9, 8)} Yes, no x-coordinate is repeated.

Give the domain & range of each relation. Is it a function? Finding Domain & Range Give the domain & range of each relation. Is it a function? Example 1 Example 2 {(3, -6), (1, 3), (-2, 4), (0,3), (1, -2), (3, 0)} x y 1 -1 5 3

Vertical Line Test Vertical Line Test: If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function.

Give the domain & range of each relation. Is it a function? Finding Domain & Range Give the domain & range of each relation. Is it a function?

Give the domain & range of each relation. Is it a function? Finding Domain & Range Give the domain & range of each relation. Is it a function? x y . . . .

Does the graph represent a function? Name the domain and range. x y Function: Yes D: All real numbers R: All real numbers R: y ≥ -6 x y

Does the graph represent a function? Name the domain and range. x y Function: No D: x ≥ 1/2 R: All real numbers D: All real numbers x y

Function Notation When we know that a relation is a function, the “y” in the equation can be replaced with f(x). f(x) is simply a notation to designate a function. It is pronounced ‘f’ of ‘x’. The ‘f’ names the function, the ‘x’ tells the variable that is being used. The parenthesis DO NOT mean multiplication! f(x) is another name for y. Sometimes other letters such as g, h or capital letters F, G and H are used to name functions.

Using Function Notation Find the value of each function. If g(s) = 2s + 3, find g(-2). If h(x) = x2 - x + 7, find h(2). If f(x) = -x2 + 5x – 3 find f(q)

Homework Page 457-458 #’s 12, 13, 18, 19, 35, 36, 37, 46