Question

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

Answer 1

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]}

Answer 2

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]}