This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Algebra 2 Name: _________________________________
8.4 – 8.6 Quiz Review Logarithmic Functions & Their Properties ♦LEARNING TARGET – 8.4 LOGARITHMIC FUNCTIONS♦ Rewrite the following logarithmic equations in exponential form. 1. log! 25 = 2 2. log! 81 = 4 3. log!
!!"= −2
4. log! 1 = 0 5. log! 512 = 𝑥 6. log!
!!"= −3
Rewrite the following exponential equations in logarithmic form. 7. 9! = 81 8. 2!! = !
! 9. 10! = 100,000
Evaluate and simplify the common/natural logarithms. 10. log 10! 11. 𝑒!" !! 12. 10!"#!.!
13. ln 𝑒!! 14. 15!"#!" !! 15. log 1000000
16. log!8! 17. log!16! 18. log!4!
!
2
Find the inverse of each equation. 19. 𝑦 = 𝑒! 20. 𝑦 = log(𝑥 − 2) 21. 𝑦 = log! 𝑥 − 4 22. 𝑦 = ln(2𝑥 + 1) 23. 𝑦 = 𝑒!! 24. 𝑦 = 4! + 1 ♦LEARNING TARGET – 8.5 GRAPHS OF EXPONENTIAL & LOGARITHMIC FUNCTIONS♦ Graph each logarithmic function. Find the y-intercept and the asymptote. Then describe how the graph is transformed from the graph of its parent function. 25. Parent: 𝑓 𝑥 = 2! 26. Parent: 𝑓 𝑥 = 2! Transformed: 𝑔 𝑥 = 2!!! Transformed: 𝑔 𝑥 = 2! − 3
Write each transformed function. 29. The function 𝑓 𝑥 = !
!
! is translated 4 units right, reflected across the x-axis, and vertically stretched by a
factor of 1.5. 30. The function 𝑓 𝑥 = ln 𝑥 is translated 3 units left, vertically compressed by a factor of !
! and translated 5 units
down. 31. The function 𝑓 𝑥 = 𝑒! is reflected across the y-axis and translated 1 unit right. Match each order of transformation of 𝒇 𝒙 = 𝒆𝒙 with its transformed function. 32. ____________ stretched vertically by a factor of 2 and translated 5 units down. 33.____________ stretched vertically by a factor of 2, translated 1 unit left, and translated 5 units up. 34. ____________ reflected across the x-axis, stretched vertically by a factor of 2, and translated 5 units down. 35. ____________ stretched vertically by a factor of 2, translated 1 unit to the right, and translated 5 units up. 36. ____________ reflected across the x-axis, stretched vertically by a factor of 2, translated 1 unit to the left, and translated 5 units down.
A. 𝑔 𝑥 = −2𝑒! − 5
B. 𝑔 𝑥 = 2𝑒! − 5
C. 𝑔 𝑥 = 2𝑒!!! + 5
D. 𝑔 𝑥 = 2𝑒!!! + 5
E. 𝑔 𝑥 = −2𝑒!!! − 5
MATCH the following functions to the letter of their corresponding graphs. 37. 𝑓 𝑥 = 2! − 4 38. 𝑔 𝑥 = 𝑒! + 4 39. ℎ 𝑥 = log!(𝑥 − 4)