Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

Sketch the graph of $y=\frac{1}{x}$.

Step-by-Step Solution

Answer

The graph of $y=\frac{1}{x}$ is:

Step 1. Given information

We have been given $y=\frac{1}{x}$.

We have to sketch it.

Step 2. Find the intercepts.

Put $x=0$ in $y=\frac{1}{x}$ to find y-intercept.

If we let $x=0$, we obtain a $0$ in the denominator, which is not defined. We conclude that there is no y-intercept.

Put $y=0$ in $y=\frac{1}{x}$ to find x-intercept.

If we let $y=0$, we get the equation $\frac{1}{x}=0$ which has no solution. We conclude that there is no x-intercept. The graph of $y=\frac{1}{x}$ does not cross or touch the coordinate axes.

Step 3. Find the points satisfying the equation

Find few points satisfying the equation $y=\frac{1}{x}$.

x	$y=\frac{1}{x}$	(x , y)
$\frac{1}{2}$	2	$(\frac{1}{2},2)$
1	1	$(1,1)$
2	$\frac{1}{2}$	$(2,\frac{1}{2})$
3	$\frac{1}{3}$	$(3,\frac{1}{3})$
$-\frac{1}{2}$	- 2	$(-\frac{1}{2},-2)$
$-\frac{1}{3}$	$-3$	$(-\frac{1}{3},-3)$
$-1$	$-1$	$(-1,-1)$
$-2$	$-\frac{1}{2}$	$(-2,-\frac{1}{2})$

Step 4. Sketch the graph

We get the following graph using the points: