Lesson 12-2Exponential & Logarithmic

FunctionsObjectivesStudents will:Graph exponential functionsGraph logarithmic functions

Exponential Functions

f(x) = ax (variable as exponent)

a: positive, real #; a ≠ 1; the base

Graphs:

f(x) > 0 (y-values)

Must pass through (0, 1)

Curve:

a < 1 → decreasing

a > 1 → increasing

Use table to get more points

(0, 1)

y = 10xy = 3x

x

y

10

1x

y

2

1

Example 1

Logarithmic Functions

Function (calculator is base 10)

General function:

)8(log

)1(log

)1000(log

)100(log

2

10

10

10

yxa log

Exponential

(1, 0)

Passes through (1, 0)

Graph is inverse (reflection) of an exponential

or xa y

Graphing Logs: Graph (1, 0) Write as exponential Write inverse function (switch x & y) Make table of inverse Switch x & y values to get Log’s values

y = log2xExample 2: Graph

y = log6x

HW 115 & 116