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

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

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

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

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

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

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) ?

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

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.