How would you use your calculator to solve

How would you use your calculator to solve 52? Input Press: 5 Output x 2 25 The number you entered is the input number (or x-value on a graph). The result is the output number (or yvalue on a graph). The x 2 key illustrates the idea of a function.

A function is a relation that gives a single output number for every valid input number. A relation is a rule that produces one or more output numbers for every valid input number. There are many ways to represent relations: Graph Equation Table of values A set of ordered pairs Mapping These are all ways of showing a relationship between two variables.

A function is a rule that gives a single output number for every valid input number. To help remember & understand the definition: Think of your input number, usually your x -coordinate, as a letter. Think of your output number, usually your y-coordinate, as a mailbox.

A function is a rule that gives a single output number for every valid input number. Input number Output number Can you have one letter going to two different mail boxes? Not a FUNCTION

A function is a rule that gives a single output number for every valid input number. Input number Output number Can you have two different letters going to one mail box?

Are these relations or functions? x 1 2 3 4 y 5 6 7 Function & Relation x 1 2 3 4 y 5 6 7 6

Are these relations or functions? x 1 y 5 6 2 7 Not a Function but a Relation x 1 2 1 1 y 5 6 7 6

Are these relations or functions? x y 1 5 2 6 3 8 11 Not a function But a relation x 1 2 2 3 y 5 6 11 8

In words: Double the number and add 3 As an equation: y = 2 x + 3 As a table of values: x y -2 -1 -1 1 0 3 1 5 These all represent the SAME function! As a set of ordered pairs: (-2, -1) (-1, 1) (0, 3) (1, 5) (2, 7) (3, 9)

Lesson 5. 2 (PART 2) Math 10 C

Functional Notation An equation that is a function may be expressed using functional notation. The notation f(x) (read “f of (x)”) represents the variable y.

Functional Notation Cont’d Example: y = 2 x + 6 can be written as f(x) = 2 x + 6. Given the equation y = 2 x + 6, evaluate when x = 3. y = 2(3) + 6 y = 12

Functional Notation Con’t For the function f(x) = 2 x + 6, the notation f(3) means that the variable x is replaced with the value of 3. f(x) = 2 x + 6 f(3) = 2(3) + 6 f(3) = 12

Evaluating Functions Given f(x) = 4 x + 8, find each: 1. f(2) = 4(2) + 8 = 16 2. f(a +1) = 4(a + 1) + 8 = 4 a + 4 + 8 = 4 a + 12 3. f( 4 a) = 4(-4 a) + 8 = -16 a+ 8

Evaluating More Functions If f(x) = 3 x 1, and g(x) = 5 x + 3, find each: 1. f(2) + g(3) = [3(2) -1] + [5(3) + 3] = 6 - 1 + 15 + 3 = 23 2. f(4) - g(-2) = [3(4) - 1] - [5(-2) + 3] = 11 - (-7) = 18 3. 3 f(1) + 2 g(2) = 3[3(1) - 1] + 2[5(2) + 3] = 6 + 26 = 32

5. 2 QUESTIONS: MUST BE DONE FOR MONDAY!