1. Lesson 3. 8 Concept: Building Functions EQ: How can we build functions
Lesson 3.8 Concept: Building Functions EQ: How can we build functions? F.BF.1b Vocabulary: input, output, like terms, distributive property

2. Multiplying Functions
Example 7: If f(x) = 4x – 1 and g(x) = -3x + 6, what is the result of multiplying the two functions? What is f(x)  g(x)? X
f(x)
g(x)
f(x)  g(x) -2 -9 12
-108 -1 -5 9
-45 6 -6 1 3

3. Example 7, continued What is 𝑓 −1 ∗𝑔(−1)? What is 𝑓 0 ∗𝑔(−2)?
𝑓 −1 ∗𝑔(−1) = −5  9 = −45
What is 𝑓 0 ∗𝑔(−2)?
𝑓 0 ∗𝑔(−2) = −1  12 = −12 X
f(x)
g(x)
f(x)  g(x) -2 -9 12
-108 -1 -5 9
-45 6 -6 1 3

4. Example 8
Example 8: If j 𝑥 =3𝑥−5 and z 𝑥 =− 3 𝑥 +2, what is the result of multiplying the two functions? What is 𝑗 𝑥 ∗𝑧(𝑥)? X
j(x)
z(x)
j(x)  z(x) -2
-11
1.89
-20.79 -1 -8
1.67
-13.36 -5 1 2

5. Example 8, continued What is j −1 ∗𝑧 1 ? What is j 0 ∗𝑧 −2 ?
𝑗 −1 ∗𝑧 1 =−8∗−1=8
What is j 0 ∗𝑧 −2 ?
𝑗 0 ∗𝑧 −2 =−5∗1.89=−9.45

6. Dividing Functions
Example 9: If c(𝑥) = −5𝑥 + 2 and k(𝑥) = 𝑥 – 6, what is the result of dividing the two functions? What is 𝑐(𝑥) 𝑘(𝑥) ? X
c(x)
k(x)
c(x)/k(x) -2 12 -8
-3/2 = -1.5 -1 7 -7
7/-7 = -1 2 -6
-1/3 = -0.3 1 -3 -5
3/5 = 0.6
Add in example like #18 on test. Include exponential

7. Example 9, continued What is 𝑐(−1) 𝑘(−1) ? What is 𝑐(0) 𝑘(−2) ? X c(x)
k(x)
c(x)  k(x) -2 12 -8
-3/2 = -1.5 -1 7 -7
7/-7 = -1 2 -6
-1/3 = -0.3 1 -3 -5
3/5 = 0.6
What is 𝑐(−1) 𝑘(−1) ?
What is 𝑐(0) 𝑘(−2) ?

8. You Try! Given m 𝑥 =−3𝑥+2 and n 𝑥 =4𝑥−1 5. Find m 2 ∗𝑛(3).

9. 3-2-1
List three things you learned in this lesson, two things you would tell a friend who was out sick, and one question you still have.