Chapter 3.3, Problem 106E

To determine

To match:

The given functions with their graphs.

Answer to Problem 106E

• $y=\ln 2$ matches with the graph A
• $y=\ln x$ matches with the graph B
• $y=\ln x^2$ matches with the graph D
• $y=\ln 2x$ matches with the graph C

Explanation of Solution

Given:

Three functions: $y=\ln x,y=\ln x^2,y=\ln 2x,\text{ and }y=\ln 2$ and the graphs:

  

We have a function $y=\ln 2$ which is a constant function. Therefore, its graph will have to be a horizontal line. We only have one horizontal line among the given graphs, so the graph A would be for the function $y=\ln 2$ .

The graph of $y=\ln x$ is the regular logarithm graph. It will be steeper than the graph of $y=\ln x^2$ between 0 and 1, but for the values beyond 1, the graph of $y=\ln x^2$ will be steeper than the graph of $y=\ln x$ . Therefore, B is the graph of $y=\ln x$ and D is the graph of $y=\ln x^2$ . That leaves us with the function $y=\ln 2x$ and the graph C, which makes complete sense because the graph of $y=\ln 2x$ is supposed to be horizontally compressed compared to the graph of $y=\ln x$ , and the graph C satisfies that condition.