Question

Graphing Logarithmic Function In Exercise,sketch the graph of the function.See example 1.

y = 5 + In x

Answer 1

The graph of given function is shown below.

Explanation:

The parent natural logarithmic function is

`f(x)=\ln x`

The given function is

`y=5+\ln x`

It means

`y=5+f(x)` .... (1)

The translation is defined as

`g(x)=kf(x+a)+b` .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2) we get

`b=5`

It means the graph of parent function shifts 5 units up to get the graph of given function.

Table of values:

x y

0.25 3.614

0.5 4.307

1 5

2 5.693

Plot these points on a coordinate plane connect then by a free hand curve.

The graph of given function is shown below.