2 1 Graphing Linear Relations and Functions Objectives
2 -1: Graphing Linear Relations and Functions Objectives: • Understand, draw, and determine if a relation is a function. • Graph & write linear equations, determine domain and range. • Understand function notation NOTES CH 2. 1 Functions
Relations & Functions- I. VOCAB Relation: a set of ordered pairs Domain: the set of x-coordinates (all the values that x can be!) Range: the set of y-coordinates (all the values that y can be!) **When writing the domain and range, do not NOTES CH 2. 1 Functions repeat values. **
Relations and Functions EX 1: Given the relation: {(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} NOTES CH 2. 1 Functions
Relations and Functions II. Representations • Relations can be written in several ways: ordered pairs, table, graph, or mapping. • We have already seen relations represented as ordered pairs. NOTES CH 2. 1 Functions
Table EX 2: {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} NOTES CH 2. 1 Functions
Mapping • Create two ovals with the domain on the left and the range on the right. • Elements are not repeated. • Connect elements of the domain with the corresponding elements in the range by drawing an arrow. NOTES CH 2. 1 Functions
Mapping EX 3: {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} D R 2 -6 1���� 0 3 4 0 NOTES CH 2. 1 Functions
Mapping diagrams • Make an mapping diagram. • EX 4: {(1, 2), (-1, 4), (0, 2), (4, -7)} • ��See board. • EX 5: {(2, 3), (-1, -5), (2, 6)} • See board. NOTES CH 2. 1 Functions
III. Functions • 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. NOTES CH 2. 1 Functions
Do the ordered pairs represent a function? Make a mapping diagram. EX 6. {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} No, 3 is repeated in the domain. EX 7. {(4, 1), (5, 2), (8, 2), (9, 8)} Yes, no x-coordinate is repeated. NOTES CH 2. 1 Functions
When given a graph, is it a function? 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. Domain: all values x can be. “Where does the graph stop to the left and to the right? ” Range: all values y can be. “ Where does the graph stop looking up and down? ” NOTES CH 2. 1 Functions
Does the graph represent a function? Name the domain and range. Yes D: all reals R: all reals EX 8 x y EX 9 x y Yes D: all reals R: y ≥ -6 NOTES CH 2. 1 Functions
Does the graph represent a function? Name the domain and range. EX 10 x No D: x ≥ 1/2 R: all reals x No D: all reals R: all reals y EX 11 y NOTES CH 2. 1 Functions
Does the graph represent a function? Name the domain and range. EX 12 x Yes D: all reals R: y ≥ -6 x No D: x = 2 R: all reals y EX 13 y NOTES CH 2. 1 Functions
IV. 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. NOTES CH 2. 1 Functions
Value of a Function Since the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2. EX 14. Find f(4): f(4) = 4 - 2 f(4) = 2 NOTES CH 2. 1 Functions
Value of a Function EX 15. If g(s) = 2 s + 3, find g(-2) = 2(-2) + 3 =-4 + 3 = -1 g(-2) = -1 NOTES CH 2. 1 Functions
Value of a Function EX 16. If h(x) = x 2 - x + 7, find h(2 c) = (2 c)2 – (2 c) + 7 = 4 c 2 - 2 c + 7 NOTES CH 2. 1 Functions
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