Q. 21 - Precalculus Enhanced with Graphing Utilities

Question

Sketch the graph of each function. Be sure to label three points on the graph. 

$f\left(x\right)=\frac{1}{x}$

Step-by-Step Solution

Answer

The graph is 

Step 1. Given information.

The given function is,

$f\left(x\right)=\frac{1}{x}$.

Step 2. Finding the symmetry.

Now substituting $x=-x$ in the given function then,

$$\begin{gathered} f(-x)=\frac{1}{-x} \\ =-\frac{1}{x} \\ =-f\left(x\right) \end{gathered}$$

Therefore, the function is an odd function and symmetric with respect to the origin.

Step 3. Finding the ordered pairs.

Using the point plotting method we get,

$x$	$$\begin{gathered} y=f\left(x\right) \\ =\frac{1}{x} \end{gathered}$$	$\left(x,y\right)$
$-1$	$$\begin{gathered} y=\frac{1}{-1} \\ =-1 \end{gathered}$$	$\left(-1,-1\right)$
$1$	$$\begin{gathered} y=\frac{1}{1} \\ =1 \end{gathered}$$	$\left(1,1\right)$
$2$	$y=\frac{1}{2}$	$\left(2,\frac{1}{2}\right)$

Step 4. Plotting the points on a graph.

The graph is