Example 1: easy
graph1
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f(x)=log(x-2)+3
First, we need to describe the transformations. 1. Up 3 units 2. Right 2 units Now we will apply them to the basic points. (0,-4) -> (2,-1) (2,1) -> (4,4) (4,2) -> (6,5) Now graph! Example 2: Medium f(x)=2log(1/2x+4)-5 First, let's describe the transformstions 1. Vertical stretch by factor of 2 2. Horizontal stretch by factor of 2 3. 4 units left 4. 5 units down Now let's transfer into the table. (0,-4) -> (-4,-13) (2,1) -> (0,-3) (4,2) -> (4,-1) Now graph! Example 3: Hard See if you can do this on your own! f(x): -3log(-1/4x-2)-8 Real Life Application The very first earthquake recorded was equal to f(x)=log2(x). A recent earthquake magnitude in California measured f(x)= 4log(1/7x+12)+6. Seismologists want to compare to the first earthquake. 1. Find the transformstions and then graph |