Algebra 2A Big Ideas 7B
|
These tables are from the Algebra 2 online textbook.
Table #1 -- From pre-Lesson 6.1 page 360
Table #2 -- From Lesson 7-4 pages 462 and 464
Table #3 -- From Lesson 7-2 page 444
Table #4 -- From Lesson 7-3 page 455
Hints
1. Remember that for all of these equations, a, b, h, and k represent constant values. The only variables are x and y.
Part 1
Using algebra steps change function f1 so that it has the form y = abx which is a stretch or compression as appears in table #3 above. You will need to use the properties of exponents in table #1.
Using algebra steps change function f1 so that it has the form y = abx which is a stretch or compression as appears in table #3 above. You will need to use the properties of exponents in table #1.
Part 2
Find the inverse function of f1. You will need the properties of logarithms in table #2. Then use algebra steps to change the inverse function so that it has the form y = logb (x - h) + k. This is a translation of function g, as appears in table #4.
Find the inverse function of f1. You will need the properties of logarithms in table #2. Then use algebra steps to change the inverse function so that it has the form y = logb (x - h) + k. This is a translation of function g, as appears in table #4.
Part 3
In part 2 you already found the inverse function of f1. So just analyze its form and explain why it is not a stretch or compression of function g.
In part 2 you already found the inverse function of f1. So just analyze its form and explain why it is not a stretch or compression of function g.
Part 4
Use the change of base formula in table #2 to change function h so that it has the form y = a logbx. This is a stretch or compression of function g as appears in table #4.
Use the change of base formula in table #2 to change function h so that it has the form y = a logbx. This is a stretch or compression of function g as appears in table #4.