Chapter 5, Problem 1RE

Sketching a Graph In Exercises 1 and 2, sketch the graph of the function and state its domain.

$f(x)=\ln x-3$

To determine

To graph: The function $f\left(x\right)=\ln x-3$ and to find its domain.

Explanation of Solution

Given:

The function to be plotted is $f\left(x\right)=\ln x-3$.

Graph:

Use Ti-83 to plot the graph of the function:

Step 1: Press the $\boxed{Y=}$ key, then there will appear the equations for $y$.

Step 2: Enter the equations in ${\text{Y}}_{\text{1}}$. Here, $f\left(x\right)=\ln x-3$

Step 3: Press $\boxed{WINDOW}$ and then edit the values as

$\begin{array}{l}X\min =-5\\ X\max =6\\ XScale=1\\ Y\min =-5\\ Y\max =5\\ YScale=1\end{array}$

Step 4: Press the $\boxed{GRAPH}$ key to plot the graph. The graph is

Interpretation:

The domain of the function $f\left(x\right)=\ln x-3$ is $\left(0,\infty \right)$ and vertical asymptote is $x=0$ and the vertical shift is 3 units downwards.