1. Operations on Functions
f(x) + g(x)
f(x) ∙ g(x)
f(x) ÷ g(x)
f(x) - g(x)
ƒ(g(x))
Operations on Functions
Lesson 2.5

2. Operations on 𝒇(𝒙) Find 𝟒𝒇(𝒙) [𝒇 𝒙 ] =[𝟐𝒙+𝟑] 𝟒[𝒇 𝒙 ] =𝟒[𝟐𝒙+𝟑]
Rewrite with brackets around entire 𝒇(𝒙).
Perform operation on entire quantity.
Simplify.
Find 𝟒𝒇(𝒙)
[𝒇 𝒙 ]
=[𝟐𝒙+𝟑]
𝟒[𝒇 𝒙 ]
=𝟒[𝟐𝒙+𝟑]
Which variable is 4 being added to?
What do I mean when I say “entire dependent variable”?

3. Practice Complete the following problem at your table.
𝑔 𝑥 = 1 2 𝑥−2 Find 6𝑔 𝑥 −8
ANSWER: 6𝑔 𝑥 −8=3𝑥−20

4. Independent Practice
Complete problem set A independently.

5. 𝑓 𝒙 =2𝒙+3 𝑓(𝟒𝒙) =2 𝟒𝒙 +3 Operations on 𝑥 Find 𝑓(𝟒𝒙)
Rewrite with space instead of x.
Substitute input into that space.
Simplify.
𝑓 𝒙 =2𝒙+3
Find 𝑓(𝟒𝒙)
𝑓(𝟒𝒙)
=2 𝟒𝒙 +3
Which variable is 4 being added to?
What will we substitute in for parentheses?

6. Practice Complete the following problem at your table.
𝑔 𝑥 = 1 2 𝑥−2 Find 𝑔(6𝑥−8)
ANSWER: 𝑔 6𝑥−8 =3𝑥−6

7. Independent Practice
Complete problem set B independently.

8. Operations on multiple functions: Adding and Subtracting
Find:
Sometimes written:
𝟐𝒙+𝟓
− 𝒙 𝟐 −𝟑𝒙−𝟏
( )
What is being subtracted from 2x+5?
If they say g(x), say what is g(x)?
How do I write that I am subtracting 𝑥 2 −3𝑥−1? R
Remember to subtract entire quantity (distribute the negative)!

9. Operations on multiple functions: Multiplying
Find (𝑓∙𝑔)(𝑥), fully simplified.

10. Practice Complete the following problems independently.
𝑔 𝑥 =2𝑥−4 and ℎ 𝑥 =−2𝑥+5. Find (ℎ−𝑔)(𝑥).
𝑔 𝑥 =2𝑥−4 and ℎ 𝑥 =−2𝑥+5. Find (𝑔∙ℎ)(𝑥).
−𝟐𝒙+𝟗
−𝟒 𝒙 𝟐 +𝟏𝟖𝒙−𝟐𝟎

11. Independent Practice
Complete problem set C independently.

12. Operations on Functions
f(x) + g(x)
f(x) ∙ g(x)
f(x) ÷ g(x)
f(x) - g(x)
ƒ(g(x))
Operations on Functions
Lesson 2.5b

13. DO NOW Review for the quiz today:
Silently re-read and annotate your notes, HW assignments and classwork. Highlight key points and write down reminders for yourself.

14. Oral Drill Function or Not? {(6, -1), (-2, -3), (1,8), (-2,-5)} Notx Y a X b c d Z

15. Oral Drill
Function or Not?
Function

16. Oral Drill Domain and range of the following relations:
{(6, -1), (-2, -3), (1,8), (-2,-5)}
Domain: {6, -2, 1}
Range: {-1, -3, 8, -5}

17. Oral Drill Domain and range of the following relations:
Domain: {a, b, c, d}
Range: {X, Y, Z} x Y a X b c d Z

18. Oral Drill Domain and range of the following relations:
Domain: all real #
Range: y ≤4

19. Oral Drill If f(x) = 3x+4, what is –f(x)? -f(x) = -3x – 4

20. Oral Drill
Describe the transformations of h(x) = −5 − 1 3 𝑥+3 −2 -horizontal stretch by a factor of 1 3 -reflection about the y-axis -horizontal translation 3 units to the left -vertical stretch by a factor of 5 -reflection about the x-axis -vertical translation 2 units down

21. Quiz When you finish, organize your binder
If you have extra time, please help organize a partner’s binder

22. Review 𝑓 𝑥 =3𝑥−5. 𝐹𝑖𝑛𝑑 −𝑓 𝑥 Is the input or output changing?
Input – independent variable
Put a space where the original input is!
𝑓 =3 −5
Substitute the new input.
𝑓 𝑥+1 =3 𝑥+1 −5
=3𝑥+3 −5
=3𝑥 −2

23. Review 𝑓 𝑥 =3𝑥−5. 𝐹𝑖𝑛𝑑 𝑓 𝑥+1 Is the input or output changing?
Output – dependent variable
Write the output, then operate!
𝑓 𝑥 =3𝑥−5
−𝑓 𝑥 =− 3𝑥−5
−𝑓 𝑥 =−3𝑥+5

24. Representing Operations Graphically
Use the graph to find f(-2) + g(-2).
Check your work by finding
f(x) + g(x) algebraically. Then
evaluate for x = -2 
TIME PERMITTING 

25. Representing Operations Graphically
𝑓 𝑥 =𝑥−2
𝑔 𝑥 =−𝑥+3
Use the graph to find g(0) x f(0).
g(0) x f(0)
3 × -2 -6
Check your work by finding
g(x) x f(x) algebraically. Then
evaluate for x=0
(𝑥−2)(−𝑥+3)
−𝑥 2 +5𝑥−6
When x= 0: − −6 −6