4.3 Function Rules, Tables, and Graphs Standard: SWBAT understand relation and a function; determine if a given relation defines a function

Mini Quiz 35 1. Is this relation a function: {(5, 3), (-2, 3), (5, 3), (4, 3)}? Explain. 2. Find the domain and range of the relation in problem 1. 3. Is this relation a function? Explain.

Quick Review 1. How do you find the domain and the range? Domain are the x’s, Range are the y’s 2. How do you tell if a relation is a function? “Every x has only one y”. Check if x repeats/the vertical line test. 3. a) Is this a function? Why? {(3, 0), (-2, 1), (0, -1), (-3, 2)} Yes, x doesn’t repeat. b) Find the domain and range. Domain: 3, -2, 0, -3 Range: 0, 1, -1,2 4. a) Is the table a function? Why? No, x repeats and you get two different y Domain: -3, 6, 8 Range: -5, 7, 4, -2

Evaluating a Function Rule The notation f(x) is the same as y (i.e. f(x) = y) 1. Evaluate f(x) = -3x – 10 for the domain {6} f(6) = -3(6) – 10 f(6) = -18 – 10 f(6) = -28

Evaluating a Function Rule The notation f(x) is the same as y (i.e. f(x) = y) 2. Evaluate f(x) = -x – 6 for the domain {-4} f(-4) = -(-4) – 6 f(-4) = 4-6 f(-4) = -2

Evaluating a Function Rule The notation f(x) is the same as y (i.e. f(x) = y) 3. Evaluate f(x) = x – 10 for the domain {-2} f(-2) = (-2) – 10 f(-2) = -1 – 10 f(-2) = -11

Graphing Equations using a Table Directions: Pick a number to plug in for x (usually “0”) Replace the x and calculate y Graph the ordered pair Repeat steps 1 - 3 at least 2 more times (to get the shape of the graph) Connect the points to draw the graph

Using Tables Find the domain and range. x 2x - 3 y 2(0) – 3 = 0 – 3 -3 4. Model the function rule y = 2x - 3 x 2x - 3 y 2(0) – 3 = 0 – 3 -3 1 2(1) - 3 = 2 – 3 -1 -1 2(-1) - 3 = -2 – 3 -5

Using Tables Find the domain and range. x -2x + 5 f(x) 5. Model the function rule f(x) = - 2x + 5 x -2x + 5 f(x)

Using Tables Find the domain and range. - x + 1 x y 6. Model the function rule y = - x + 1 - x + 1 x y

Domain and Relations Graph the function and determine the domain and range. 7. y = |x|

Domain and Relations Graph the function and determine the domain and range. 8. f(x) =

Wrap Up Evaluating Function Using a Table to Graph Determining Domain and Function Determining Domain and Range HW: P. 190 #1-17 odd, 21, 25, 61-67 all DLUQ: What do you need to make to graph a function?