Question

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

Answer 1

Answer:

The graph of given function is shown below.

Step-by-step 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.