How do you sketch the graph of #y=log_2(x+2)#?

2 Answers
Nov 29, 2016

The graph of #y# is the standard graph of #lnx# transformed 2 units left and scaled by #1/ln2#

Explanation:

To change the base of the log to base e:

#log_2 x = ln(x)/ln2#

In this example #y=log_2(x+2)#

#:. y= ln(x+2)/ln2#

The graph of #y# is the standard graph of #lnx# transformed 2 units left and scaled by #1/ln2#

#y# is defined for #x> -2#
#y# has a single zero at #x=-1#
#y=1# at #x=0#

The graph of #y# is shown below

graph{ln(x+2)/ln2 [-10, 10, -5, 5]}

Nov 29, 2016

x-intercept is -1; y-intercept is 1.
As #x to-2, y to -oo#; as #x to oo, y to oo#. Graph for the inverse #x=2^y-1# is inserted.

Explanation:

Cuts axes at (-1, 0) and (0, 1). x = -2 is the asymptote.

For graphing, I have used the inverse #x = 2^y-1#.

graph{2^y-x-2=0 [-10, 10, -5, 5]}