Period 1: 6.3- Transformations

Hi everyone :)

so on Friday we learned about transformations to logarithmic graphs, pretty much taking all our knowledge of transformations and applying it to a new type of graph. We have to remember a few things in order to graph correctly.

STEPS to apply multiple transformations

1. Ensure the function is in the form of f(x) = a log [k(x-d)] + c
***don't fall for the trap where the equation is not in factored form!! it will be on our test and exam so watch out for it!!***
2. apply vertical stretches, compressions, and reflections
3. apply horizontal stretches, compressions, and reflections
4. apply horizontal translations
5. apply vertical translations

mapping rule always begins with (x,y)--->

Note: We must keep in mind that the vertical asymptote depends on the horizontal shift of the equation. Any other stretch or compression, or vertical shift on the graph will not affect the vertical asymptote.

A logarithmic graph's key features:
- the domain is affected because of the asymptotes
- there is no horizontal asymptote
- x-intercepts can be found my solving for x when y=0 (using skills learnt in 6.2 with logarithms) for example:

y=-2log[1/2(x+6)]-3
0=-2log[1/2(x+6)]-3
-3/2=log[1/2(x+6)]
10^-3/2= [1/2(x+6)]
0.03162/.5 = x+6
0.06325 = x+6
-5.9368 = x

therefore, -5.9368 is the x-intercept.

- the table of values are different for this type of graph:
we must make 3 different tables in order to graph
the first one is our base exponential function
the second one is our base parent function of the logarithmic function
the third one is our table of values with all the transformations applied