1. Module 1 Day 1
Evaluating Functions

2. Evaluating functions:
Plug the value in for the variable
Evaluate the function given the value
Example 𝑓(𝑥) = 𝑥 find 𝑓(3)
𝑓(3)= 14

3. Evaluating functions:
Example: 𝑓 𝑥 = −3𝑥 2 −2𝑥 find 𝑓( 𝑥 2 )
𝑓 𝑥 2 =−3 𝑥 4 −2 𝑥 2
Example: g 𝑥 =12 𝑥 find g(−2𝑥)
𝑓 −2𝑥 =48 𝑥 2 +6
Example: h 𝑥 =3𝑥+5 find h(2𝑥+1)
ℎ(2𝑥+1)=6𝑥+11

4. Arithmetic Sequences Adding or subtracting to get the next term
The pattern is called the common difference.

5. Geometric Sequences Multiplying to get the next term
The pattern is called the common ratio

6. Explicit Formula: Arithmetic
Explicit is used to find any term in the sequence
𝑦 = 𝑚𝑥 + 𝑏 or 𝑓(𝑥)= 𝑚𝑥 + 𝑏
𝑚 = common difference
𝑏 = zero term
Plug in values to equation
Example: Write the explicit equation:
2, −4, −10, −16…
𝑓(𝑥)= −6𝑥 +8

7. Explicit Formula: Geometric
Explicit is used to find any term in the sequence
𝑓(𝑥)= 𝑎∙ 𝑏 𝑥
𝑎 = zero term
𝑏= common ratio
Example: Write the explicit equation:
6, -24, 96, -384…
𝑓 𝑥 = −3 2 −4 𝑥

8. Clickers

9. Explicit Formula: Geometric
Example: Write the explicit equation given:
2, -4, 8, -16….. And f(1)= 2

10. Explicit Formula: Geometric
Example: Write the explicit equation given 𝑓(1) = 2, common ratio is −4
𝑓 𝑥 = −1 2 ∙ −4 𝑥 𝑜𝑟 𝑓 𝑥 =2∙ −4 𝑥−1
Find 𝑓(5)
𝑓(5)= 512

11. Check For Understanding:
If f(x)= 2x2 -3x – 4, find f(-4)
f(-4)= 40
Find the common difference: 8, 2, -4, -10…
CD= -6
Write the explicit equation from the sequence above.
y= -6x +14
What is the 10th term?
-46
Write the recursive formula:
f(x)= f(x-1) - 6

12. Check For Understanding:
Find the common ratio: -3, 6, -12, 24…
CR= -2
Write the explicit equation from the sequence above.
𝑓 𝑥 =−3∙ −2 𝑥− 𝑜𝑟 𝑓 𝑥 = 3 2 ∙ (−2) 𝑥
What is the 5th term?
-48
Write the recursive formula:
f(x)= f(x-1) ∙ -2

13. Recursive Formulas: Arithmetic and Geometric
Recursive is used to find the next term from the previous term
The previous term is represented by: f(x-1) or any other variable
𝑓(𝑛) = 𝑓( 𝑛 – 1 ) +/− Common Difference or
𝑓(𝑛) = 𝑓( 𝑛 – 1 ) ∙ Common Ratio
𝑛 = the term number
Example: Determine the 2nd term if 𝑓(1) = 2 and the recursive formula given is 𝑓(𝑛) = 𝑓(𝑛−1) − 6
Answer: 𝑓(2)= −4