Graph of Logarithmic functions

1 b

1

b2

2

Graph of y = logbx b >1

If x = ------ , then y = ------

1/b -1

1 0

b 1

b2 2

-1

1/b

1 b

1

y = logbx if x > 0

b2

2

-1-b-b2

Sketch the graph of y = logb|x| b >1

If x = ------ , then y = ------

1 0

b 1

b2 2

If x = ------ , then y = ------

-1 0

-b 1

-b2 2

y = log b

(-x) if x < 0

Graph of y = logb|x| b > 1

is symmetric with respect to y-axis, that is, logb|x| is an even function.

1 1/b

-1

1/b2

-2

Graph of y = logbx b < 1

If x = ------ , then y = ------

b 1

1 0

1/b -1

1/b2 -21

b

If x = ------ , then y = ------

-1 0

-1/b -1

-1/b2 -2

1 1/b

-1

y = logbx if x > 0

1/b2

-2

-1-1/b-1/b2

Sketch the graph of y = logb|x| b < 1

If x = ------ , then y = ------

1 0

1/b -1

1/b2 -2

y = log b

(-x) if x < 0

Graph of y = logb|x| b < 1

is symmetric with respect to y-axis, that is, logb|x| is an even function.

-2 2

1

Graph of y = log5 (x+3)

If x = ------ , then y = ------

-2 0

2 1

-3

4

1

Graph of y = log0.5

(x-3)

If x = ------ , then y = ------

4 0

3.5 1

3

3.5

-2 -1

1

Graph of y = -log0.5

(x+3)

If x = ------ , then y = ------

-2 0

-1 1

-3