Chapter 3.3, Problem 108E

To determine

To match: given function with its graph.

Answer to Problem 108E

  $\begin{array}{l}A=\ln 2\\ B=\ln 2x\\ C=\ln 2x\\ D=\ln x^2\end{array}$

Explanation of Solution

Given information:

The figure shows the graphs of $y=\ln x,y=\ln x^2,y=\ln 2x$ and $y=\ln 2$ .

Calculation:

Consider the graphs below.

  

From the graphs it is clear that $A$ is the straight line graph in pink as it corresponds to the constant $\ln 2=0.693$ . So $A=\ln 2$ .

Also $B$ represents the graph in red defined by $y=\ln x$ since it passes through the point $\left(1,0\right)$ because when $x=1,y=0$ . So $B=\ln 2x$

Also $C$ represents the graph in green defined by $y=\ln 2x$ since it passes through the point $\left(0.5,0\right)$ because when $x=0.5,y=0$ . So $C=\ln 2x$

Finally $D$ represents the graph in blue defined by $y=\ln x^2$ since it passes through the point $\left(1,0\right)$ because when $x=1,y=0$ and it is a little higher than $y=\ln x$ as the variable $x$ is squared. So $D=\ln x^2$ .