Answer:
The graph of given function is shown below.
Step-by-step explanation:
The parent natural logarithmic function is
[tex]f(x)=\ln x[/tex]
The given function is
[tex]y=\frac{1}{4}\ln x[/tex]
It means
[tex]y=\frac{1}{4}f(x)[/tex] .... (1)
The translation is defined as
[tex]g(x)=kf(x+a)+b[/tex] .... (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
[tex]k=\frac{1}{4}[/tex]
It means the graph of parent function compressed vertically by factor 4 to get the graph of given function.
Table of values:
x y
0.25 -0.347
0.5 -0.173
1 0
2 0.173
Plot these points on a coordinate plane connect then by a free hand curve.
The graph of given function is shown below.
