Chapter 8

EXAMPLE 2 Connecting a geometric description of a
function to an algebraic representation
The logarithmic function y 5 log 10 x has been vertically compressed by a factor
2
of horizontally stretched by a factor of 4, and then reflected in the y-axis.
3 ,
It has also been horizontally translated so that the vertical asymptote is x 522
and then vertically translated 3 units down. Write an equation of the transformed
function, and state its domain and range.
Solution
y 5 a log 10 (k(x 2 d )) 1 c
y 5 2 3 log 10a2 1 (x 1 2)b 2 3
4
Write the general form of the
logarithmic equation.
Since the function has been
vertically compressed by a
2
factor of a 5 2 3 , 3 .
Since the function has been
horizontally stretched by a
1
factor of 4, so k 5 1 k 5 4, 4 .
The function has been reflected
in the y-axis, so k is negative.
The vertical asymptote of the
parent function is x 5 0.
Since the asymptote of
the transformed function is
x 522, the parent function
has been horizontally
translated 2 units left,
so d 522.
The function has been vertically
translated 3 units down, so
c 523.
Domain 5 5xPR 0 x ,226
Range 5 5 yPR6
The curve is to the left of the
vertical asymptote, so the
domain is x ,22.
The range is the same as the
range of the parent function.
456 8.2 Transformations of Logarithmic Functions
NEL