Take Note Concept Summary: Families of Logarithmic Functions

Problem 5 Translating y = log b x y equals , log base b , x

How does the graph of y = log 4 ( x − 3 ) + 4 y equals , log base 4 , open x minus 3 close plus 4  compare to the graph of the parent function?

Step 1	Step 2
Make a table of values for the parent function. Use the definition of logarithm.	Graph the parent function. Shift the graph to the right 3 units and up 4 units to graph y = log 4 ( x − 3 ) + 4 . y equals , log base 4 , open x minus 3 close plus 4 .
x log 4 x = y → 4 y = x log base 4 , x equals y rightwards arrow 4 y equals x y 1 16 1 sixteenth 4 − 2 = 1 16 4 super negative 2 end super , equals , 1 sixteenth − 2 negative 2 1 4 1 fourth 4 − 1 = 1 4 4 , negative to the first , equals , 1 fourth − 1 negative 1 1 4 0 = 1 4 to the , equals 1 0 4 4 1 = 4 4 to the first , equals 4 1 16 4 2 = 16 4 squared , equals 16 2	Image Long Description

Because y = log 4 ( x − 3 ) + 4 y equals , log base 4 , open x minus 3 close plus 4  translates the graph of the parent function 3 units to the right, the asymptote changes from x = 0 x equals 0  to x = x equals  3. The domain changes from x > 0 x greater than 0  to x > 3 . x greater than 3 .  The range remains all real numbers.

✓ Got It?

5. How does the graph of each function compare to the graph of the parent function?
   1. y = log 2 ( x − 3 ) + 4 y equals , log base 2 , open x minus 3 close plus 4
   2. y = 5 log 2 x y equals 5 , log base 2 , x