1A) f(x) = 2^x
i)
use what you have learned about transformations to write an equation for the function g(x), which is a function that shifts the graph of f(x) to the left 3 units. Do not just write g(x) in terms of f(x); write the equation for g(x) clearly demonstrating the transformation relationship.
ii) Write a table of values for f(x) using these values of x: -1, 0, 1, 2, 3
iii) Write a table of values for g(x) using these values of x: -4, -3, -2, -1, 0
iv) h(x) = 8(2^x) Make a table of values using the values of x: -4, -3, -2, -1, 0
v) Compare the tables in ii, iii, and iv. What observation do you make?
vi) use your knowledge of laws of exponents to explain the relationship between the graph of iii and iv. Why does this relationship exist?
2 A)
use two laws of logarithms to write login another way (you will have a combination of 2 logs)
1 = log(10)
iii) Substitute your answer from ii into the expression 1 + log x
iv) use one law of logarithms, together with your answer to iii, to write iii as a single logarithm
v) Show log =. You will be utilizing work from previous parts to write this proof