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

2. 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

3. 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 *

4. 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

5. 3. 4. Yes No  the x-value 4 has 3 different y-values x y -5 8 -3 5 -12 4.
Yes
No  the x-value 4 has 3 different y-values

6. 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.

7. 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
y2 = x + 1
No – Each x has 2 possible y values

8. 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.

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

10. 2.
Not a Function

11. 3.
Function

12. 4.
Not A Function

13. 5.
Not A Function

14. 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

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

16. 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.

17. 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 – find f(3)

18. Evaluating Functions
Substitute the number that is in the parentheses in for the variable and solve
 f(x) = 2x – 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

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

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

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

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

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

24. 6. f(x) =
Find f(6)
f(6) = − = =

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) = =

26. 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  ∙ 75
= 300
Answer: 4f(5) = 300

27. .
Teacher Copy (Magnani)
9. g(x) = 2x2 + 8
Find 𝑔(3) 𝑔(−4)
= 𝟏𝟑 𝟐𝟎

28. 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

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

30. Homework
Worksheet 3.1