Name: ____________________________________ Period: ____ Date: _________________________ You must show all work to get credit. Write your answers on the review handout. (this paper) Points possible: 20 pts. Module 15 Review 15.1 Understanding Geometric Sequences Tell whether the following are a geometric sequence, arithmetic sequence, or neither. If the sequence is geometric or arithmetic, state the common ratio or the common difference. 1. 2, 4, 6, 8, 10… 2. 3, 6, 12, 24…
Geometric/arithmetic/neither: Geometric/arithmetic/neither: Common ratio/difference: Common ratio/difference: Find the common ratio, r, for each geometric sequence and then use r to find the next 3 terms. 3. 9, -3, 1, -1/3… 4. 5, 20, 80, 320…
Common ratio: Common ratio: Next 3 terms: Next 3 terms: 15.2 Constructing Geometric Sequences Use each geometric sequence to write a recursive rule and an explicit rule. Then find the indicated term(s) of the sequence. 5. 6, 24, 96, 384, 1536… 6. 4, 12, 36, 108…
Explicit Rule: Explicit Rule: Recursive Rule: Recursive Rule: 6th term: 6th term: 15.3 Constructing Exponential Functions 7. What is the difference between a discrete and a continuous function?
Complete a table for each function using the given domain. Then graph the function using the ordered pairs from the table.
1
8. 𝑓(𝑥) = 2 ∙ 4𝑥
domain: {-2, -1, 0, 1, 2}
2 𝑥
9. 𝑓(𝑥) = 6 (3)
domain: {-1, 0, 1, 2, 3, 4}
15.4 Graphing Exponential Functions Graph the following using Desmos. Describe the end behavior of the graph. 10. 𝑦 = 3(2)𝑥 11. 𝑦 = 0.5(2)𝑥
End behavior: 12. 𝑦 = 3(0.5)𝑥
End behavior: 13. 𝑦 = −3(2)𝑥
End behavior: End behavior: State the a, b, and the y-intercept (as an ordered pair). Graph the function without a using Desmos. Describe the end behavior of the graph.
14. 𝑓(𝑥) = 3(3)𝑥
a= b= y-intercept:
15. 𝑓(𝑥) = −2(0.8)𝑥
a= b= y-intercept:
15.5 Transforming Exponential Functions 16. Describe how a, b, h, and k affect the graph.
Find the a, b, h, k, and y-intercept (written as an ordered pair). Explain how the values affect the parent function. 17. 𝑓(𝑥) = −0.25(0.6)𝑥 18. 𝑓(𝑥) = 0.4𝑥 + 5
19. 𝑦 = 2𝑥+3 − 4
20. 𝑦 = −(3)𝑥+1
