Logarithms

1
Logarithms

• Graphing

2
Learning Goal

• I will be able to graph logarithmic functions.

3
Change of Base Formula
Allows us to graph any log in the calculator,
which is only preprogrammed with common and
natural logs. Most people use c 10 or c e, so
that were using the common log or natural log.
4
Graphs of Log Functions
The log is the exponent!
Graph y log x.
y
x
1/10
-1
1
0
1
10
2
100
5
Graphs of Log Functions
Explain how the graph of y log (-x) can be
obtained from the graph of its parent function.
Reflection across y-axis
Domain Range Vertical Asymptote
x 0
6
Graphs of Log Functions
Explain how the graph of y log3 (3-x) can be
obtained from the graph of its parent function.
y log3 (-x 3) y log3 (-(x 3)) Reflection
across y-axis and shift right 3
Domain Range Vertical Asymptote
x 3
7
Graphs of Log Functions
Explain how the graph of y -3log4 (x - 5) 1
can be obtained from the graph of its parent
function.
Shift right 5, vertically stretch by a factor of
3, reflect across x-axis and shift up 1.
Domain Range Vertical Asymptote
x 5
8
Graphs of Log Functions
Use transformations!
Graph y -3log4 (x - 5) 1.
x
y log4 x
x
y
-1
1/4
5.25
4
0
1
6
1
1
4
9
-2
9
Learning Goal

• I will be able to graph logarithmic functions.

10
End of notes.

• Now do this Gateway Problem
• How has f(x) log10 (x 1) 4 been transformed
  from its parent function? Identify any
  asymptotes of the function.

A Gateway Problem is an opportunity to see if you
have mastered the learning goal. You should not
discuss the gateway problem with anyone while
doing it we need to see what you know.
11
Gateway Problem Answertranslated right 1, up 4
VA at x1

• If successful, homework is p. 195 35, 39, 43,
  45 48, 81. If not successful, homework is p.
  195 35 43 odds, 45 48, 81.