Lesson 3.1 Objective: SSBAT define and evaluate functions. Algebra 3 Lesson 3.1 Objective: SSBAT define and evaluate functions. Standards: 2.2.11C, 2.8.11B,C,D

Function A relation (set of ordered pairs) in which each number in the Domain is paired with exactly 1 number from the Range i.e.  A set of ordered pairs where no two pairs have the same x-value  The x-coordinates can NOT repeat

Function {(3, 9), (-2, 4), (1, 1), (2, 4), (-4, 16)} NOT a Function {(3, 9), (-2, 4), (1, 1), (2, 4), (-4, 16)} NOT a Function {(0, 0), (4, 2), (1, -1), (4, -2)} * 2 ordered pairs have the same x-value *

No – the x-value of 1 as two output values Examples: Are each of the following relations functions? 1. {(1,8), (2,7), (3,6), (4,5), (5,6)} 2. {(2,4), (1,10), (3,6), (1,5)} Yes No – the x-value of 1 as two output values

3. 4. Yes No  the x-value 4 has 3 different y-values x y -5 8 -3 5 -1 2 4. Yes No  the x-value 4 has 3 different y-values

Shortcut Determining if an equation represents a function Solve the equation for y If you have to take an even root ( , 4 , etc) it is NOT a fuction Otherwise it is Shortcut If the equation has y to an Odd power it IS a function. y, y3, y5, etc. If the equation has y to an Even power it’s NOT a function y2 , y4 , y6 , etc.

Yes – for each x there is only 1 y y = 1 – x2 Determine if the following represent a function 1. x2 + y = 1 Yes – for each x there is only 1 y y = 1 – x2 2. y2 = x + 1 No – Each x has 2 possible y values

Determining if a Graph represents a Function. Use the Vertical Line Test If a vertical line CAN pass through the graph, without touching it in more than one place at a time, it IS a function.

Examples: Determine if each represents a function. 1. Function

2. Not a Function

3. Function

4. Not A Function

5. Not A Function

Determining if each is a function Set of Ordered Pairs  If the x-coordinates are all different it IS a function Equation  If the y has an odd exponent it IS a function Graph  If it passes the vertical line test it IS a function

Determine if each represents a function or not. 1. {(5, -2), (7, 0), (-3, 8), (6, 0)} 5x – 4y3 = 9 3.

Function Notation f(x) Read as “f of x” For functions, y and f(x) are the same thing (just 2 different notations) It does NOT mean f times x.

f(x) means we have a function, called f, that has the variable x. Instead of saying: y = 2x – 5 , solve for when x = 3 Function Notation allows us to write: f(x) = 2x – 5 find f(3)

Evaluating Functions Substitute the number that is in the parentheses in for the variable and solve  f(x) = 2x – 5 find f(3) What it means: Let x = 3 and simplify the right side (don’t do anything to the Left side) f(3) = 2(3) – 5 = 6 – 5 = 1 So: f(3) = 1

Examples: Evaluate each. f(x) = 3x – 4 Find f(5)  let x = 5 and solve f(5) = 3(5) – 4 f(5) = 11

2. g(x) = x2 + 3x Find g(-2) g(-2) = (-2)2 + 3(-2) g(-2) = -2 Just simplify the right side

3. f(x) = -2x – 11 Find f(-3) f(-3) = -2(-3) – 11 = -5 . Teacher Copy (Magnani) 3. f(x) = -2x – 11 Find f(-3) f(-3) = -2(-3) – 11 = -5

4. f(x) = 8x + 5 Find f(x + 4) f(x + 4) = 8(x + 4) + 5 = 8x + 32 + 5 = 8x + 37

g(x + 1) = x2 + 2x + 8 5. g(x) = x2 + 7 Find g(x + 1)

6. f(x) = Find f(6) f(6) = 3 6 −4 8 6 +2 = 14 50 = 7 25

7. f(x) = 8x – 10 Find f(11) + f(-3) f(11) = 8(11) – 10 = 78 f(-3) = 8(-3) – 10 = -34 f(11) + f(-3) = 78 + -34 = 44

8. f(x) = 3x2 Find: 4f(5) 1st: Find f(5)  f(5) = 3(5)2 = 75 Teacher Copy (Magnani) 8. f(x) = 3x2 Find: 4f(5) 1st: Find f(5)  f(5) = 3(5)2 = 75 2nd: Take 4 times 75  4 ∙ 75 = 300 Answer: 4f(5) = 300

. Teacher Copy (Magnani) 9. g(x) = 2x2 + 8 Find 𝑔(3) 𝑔(−4) = 𝟏𝟑 𝟐𝟎

If f(x) = 13 – x and g(x) = 4x – 10 which is greater f(-7) or g(7)? 20 > 18 Therefore… f(-7) is Greater

On Your Own Let: f(x) = x3 + 4 1. Find f(-6) 2. Find 3f(2)

Homework Worksheet 3.1