Chapter 9.4, Problem 3E

To determine

To graph: The given function using graphing calculator.

Explanation of Solution

Given information:

The following function:

  $f\left(x\right)=\frac{2}{x-4}$ .

Graph:

Step 1:Sketch the graph using graphing utility.

Step i: Press WINDOW button to access the Window editor.

Step ii: Press $\boxed{\text{Y=}}$ button.

Step iii: Enter the expression $\frac{2}{x-4}$ which is required to graph.

Step iv: Press GRAPH button to graph the function.

The graph is obtained as:

  

Step 2: Examine the graph.

By looking at the equation, it can be determined that if $x=4$ , the function is undefined. The equation of the vertical asymptote is $x=4$ . Notice what happens to the y-values as x grows larger and as x gets smaller. The y-values approach $0$ . So, the equation for the horizontal asymptote is $y=0$ .