1. By the end of this lesson, you will know how to: Evaluate a function
5/9/2019
Day 6
Evaluating Functions
By the end of this lesson, you will know how to:
Evaluate a function
Substitute a value into a function to find the solution

2. State the Domain and Range
5/9/2019
State the Domain and Range

3. State the Domain and Range
5/9/2019
State the Domain and Range
{4, -6, 5, -4, 5}
{2, 2, 6, 8, 1}

4. Are these Functions? If no, WHY NOT??
5/9/2019
Are these Functions? If no, WHY NOT??
Input
Output -2 2 1 4 5 6

5. Are these Functions? If no, WHY NOT??
5/9/2019
Are these Functions? If no, WHY NOT??
Input
Output -2 2 1 4 5 6
YES NO

6. How would you solve this?
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
How would you solve this?
Talk with your partner.

7. What is the value of x? Evaluating a function
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
What is the value of x?

8. So, what would you do with -2?
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
What is the value of x? -2
So, what would you do with -2?
Now what?
Talk with your partner!

9. So, what would you do with -2?
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
So, what would you do with -2?
Right! Substitute it for every x in the equation!

10. Evaluating a function f(x) = x2 – 2x + 3 when x = -2
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
f(-2) = (-2 )2 – 2(-2 ) + 3
Now what?
Talk with your partner!

11. Use order of operations to solve! Solve it with your partner!
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
f(-2) = (-2 )2 – 2(-2 ) + 3
Exactly!
Use order of operations to solve!
Solve it with your partner!

12. f(-2) = – 2(-2) + 3 (-2)2 What is ? (-2)2 Evaluating a function
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
f(-2) = – 2(-2) + 3
(-2)2
What is ?
(-2)2

13. f(-2) = (-2)2 – 2(-2) + 3 f(-2) = – 2(-2) + 3 4 Evaluating a function
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
f(-2) = (-2)2 – 2(-2) + 3
f(-2) = – 2(-2) + 3 4

14. f(-2) = (-2)2 – 2(-2) + 3 f(-2) = 4 + 3 – 2(-2) What is ? – 2(-2)
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
f(-2) = (-2)2 – 2(-2) + 3
f(-2) =
– 2(-2)
What is ?
– 2(-2)

15. f(-2) = (-2)2 – 2(-2) + 3 f(-2) = 4 – 2(-2) + 3 f(-2) = + 3 4 + 4
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
f(-2) = (-2)2 – 2(-2) + 3
f(-2) = 4 – 2(-2) + 3
f(-2) =
4 + 4

16. f(-2) = (-2)2 – 2(-2) + 3 f(-2) = 4 – 2(-2) + 3 f(-2) = 4 + 4 + 3
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
f(-2) = (-2)2 – 2(-2) + 3
f(-2) = 4 – 2(-2) + 3
f(-2) =
What is ?

17. f(-2) = (-2)2 – 2(-2) + 3 f(-2) = 4 – 2(-2) + 3 f(-2) = 4 +4 + 3
5/9/2019
Evaluating a function
f(x) = x2 – 2x + 3 when x = -2
f(-2) = (-2)2 – 2(-2) + 3
f(-2) = 4 – 2(-2) + 3
f(-2) =
f(-2) = 11

18. So, how do you evaluate a function?
5/9/2019
Day 6
So, how do you evaluate a function?
g(x) = 4x2 + 3x + 5, x=4
Solve it with your partner!

19. g(x) = 4x2 + 3x + 5, x=4 Substitute 4 for x. g(4) = 4(4)2 + 3(4) + 5
5/9/2019
Day 6
g(x) = 4x2 + 3x + 5, x=4
g(x) = 4x2 + 3x + 5, x=4
Substitute 4 for x.
g(4) = 4(4)2 + 3(4) + 5

20. Use order of operations to solve.
5/9/2019
Day 6
g(x) = 4x2 + 3x + 5, x=4
g(x) = 4x2 + 3x + 5, x=4
g(4) = 4(4)2 + 3(4) + 5
Use order of operations to solve.
g(4) = 4(16) + 3(4) + 5

21. g(x) = 4x2 + 3x + 5, x=4 g(x) = 4x2 + 3x + 5, x=4
5/9/2019
Day 6
g(x) = 4x2 + 3x + 5, x=4
g(x) = 4x2 + 3x + 5, x=4
g(4) = 4(4)2 + 3(4) + 5
g(4) = 4(16) + 3(4) + 5

22. g(x) = 4x2 + 3x + 5, x=4 g(x) = 4x2 + 3x + 5, x=4
5/9/2019
Day 6
g(x) = 4x2 + 3x + 5, x=4
g(x) = 4x2 + 3x + 5, x=4
g(4) = 4(4)2 + 3(4) + 5
g(4) = 4(16) + 3(4) + 5
g(4) = (4) + 5

23. g(x) = 4x2 + 3x + 5, x=4 g(x) = 4x2 + 3x + 5, x=4
5/9/2019
Day 6
g(x) = 4x2 + 3x + 5, x=4
g(x) = 4x2 + 3x + 5, x=4
g(4) = 4(4)2 + 3(4) + 5
g(4) = 4(16) + 3(4) + 5
g(4) =

24. g(x) = 4x2 + 3x + 5, x=4 g(x) = 4x2 + 3x + 5, x=4
5/9/2019
Day 6
g(x) = 4x2 + 3x + 5, x=4
g(x) = 4x2 + 3x + 5, x=4
g(4) = 4(4)2 + 3(4) + 5
g(4) = 4(16) + 3(4) + 5
g(4) =
g(4) = 81

25. 5/9/2019
Day 6
So, what kind of mistakes do you think people might make with evaluating functions?

26. Quiz Answers 1. f(x) = 2x + 5, x = 4 f(4) = 2(4) + 5 f(4) = 8 + 5
5/9/2019
Day 6
Quiz Answers
1. f(x) = 2x + 5, x = 4
f(4) = 2(4) + 5
f(4) = 8 + 5
f(4) = 13

27. 2. f(x) = 2x2 + 5x + 4, x = 4 f(4) = 2(4)2 + 5(4) + 4
5/9/2019
Day 6
2. f(x) = 2x2 + 5x + 4, x = 4
f(4) = 2(4)2 + 5(4) + 4
f(4) = 2(16)
f(4) =
f(4) = 56

28. 3. f(x) = 3x + 2, x = 2 f(2) = 3(2) + 2 f(2) = 6 + 2 f(2) = 8
5/9/2019
Day 6
3. f(x) = 3x + 2, x = 2
f(2) = 3(2) + 2
f(2) = 6 + 2
f(2) = 8

29. 4. f(x) = -3x2 + 2x - 4, x = 2 f(2) = -3(2)2 + 2(2) – 4
5/9/2019
Day 6
4. f(x) = -3x2 + 2x - 4, x = 2
f(2) = -3(2)2 + 2(2) – 4
f(2) = -3(4) + 4 – 4
f(2) = – 4
f(2) = -8 – 4
f(2) = -12