Lesson 4-3 Warm-Up

“Function Rules, Tables, and Graphs” (4-3) What is a “function rule”? What is a “function table”? Function Rule: an equation that describes a function – You can think of a function as function rule as an input-output machine If you know the input values, you can use a function rule to find the output values (in other words, the output values depend on the input values). Function Table: a table in which shows the relation between the input and output values. Example: The following function table shows the relation of the above function rule.

“Function Rules, Tables, and Graphs” (4-3) What is “function notation”? What are the “independent and dependent variable”? Function Notation: writing a function in the form of f(x) , which is read “f of x” [in other words, replace y with f(x), g(x), h(x) or something similar] Example: Instead of y = 3x + 4, write f(x) = 3x + 4 to show that this is a function rule. Independent Variable (its value doesn’t depend on another number): the input, or x, values Dependent Variable (its value depends on another number, the independent varable): the output, or y, values

Function Rules, Tables, and Graphs LESSON 4-3 Additional Examples Evaluate the function rule ƒ(g) = –2g + 4 to find the range for the domain {–1, 3, 5}. ƒ(g) = –2g + 4 ƒ(–1) = –2(–1) + 4 ƒ(–1) = 2 + 4 ƒ(–1) = 6 ƒ(g) = –2g + 4 ƒ(3) = –2(3) + 4 ƒ(3) = –6 + 4 ƒ(3) = –2 ƒ(g) = –2g + 4 ƒ(5) = –2(5) + 4 ƒ(5) = –10 + 4 ƒ(5) = –6 The range is {–6, –2, 6}.

Model the function rule y = + 2 using a table of values and a graph. x Function Rules, Tables, and Graphs LESSON 4-3 Additional Examples Model the function rule y = + 2 using a table of values and a graph. 1 3 x Step 2: Plot the points for the ordered pairs. Step 1: Choose input value for x. Evaluate to find y. x (x, y) –3 y = (–3) + 2 = 1 (–3, 1)  0 y = (0) + 2 = 2 (0, 2)  3 y = (3) + 2 = 3 (3, 3) y = x + 2 1 3 Step 3: Join the points to form a line. (3, 3) (–3, 1) (0, 2)

Function Rules, Tables, and Graphs LESSON 4-3 Additional Examples At the local video store you can rent a video game for $3. It costs you $5 a month to operate your video game player. The total monthly cost C(v) depends on the number of video games v you rent. Use the function rule C(v) = 5 + 3v to make a table of values and a graph. (2, 11) v C(v) = 5 + 3v (v, C(v)) 0 C(0) = 5 + 3(0) = 5 (0, 5) 1 C(1) = 5 + 3(1) = 8 (1, 8) 2 C(2) = 5 + 3(2) = 11 (2, 11) (1, 8) (0, 5)

Graph the function y = |x| + 2. Function Rules, Tables, and Graphs LESSON 4-3 Additional Examples Graph the function y = |x| + 2. Make a table of values. x y = |x| + 2 (x, y) –3 y = |–3| + 2 = 5 (–3, 5) –1 y = |–1| + 2 = 3 (–1, 3) 0 y = |0| + 2 = 2 ( 0, 2) 1 y = |1| + 2 = 3 ( 1, 3) 3 y = |3| + 2 = 5 ( 3, 5) Then graph the data. (-3, 5) (3, 5) (-1, 3) (1, 3) (0, 2)

Find the domain of the relation y = . Is the relation a function? Function Rules, Tables, and Graphs LESSON 4-3 Additional Examples 1 2 – x Find the domain of the relation y = . Is the relation a function? The function is not defined for x = 2. So the domain is {x:x ≠ 2}. Since each value in the domain corresponds to exactly one value in the range. The relation is a function.

1. Model y = –2x + 4 with a table of values and a graph. Function Rules, Tables, and Graphs LESSON 4-3 Lesson Quiz 1. Model y = –2x + 4 with a table of values and a graph. x y = –2x + 4 (x, y) –1 y = –2(–1) + 4 = 6 (–1, 6) 0 y = –2(0) + 4 = 4 (0, 4) 1 y = –2(1) + 4 = 2 (1, 2) 2 y = –2(2) + 4 = 0 (2, 0) 2. Graph y = |x| – 2.