itomath.com

(4.1) The Reciprocal Function

The Reciprocal

$2 \xrightarrow{\text{reciprocal}} \frac{1}{2}$

$-3 \xrightarrow{\text{reciprocal}} -\frac{1}{3}$

$\frac{4}{5} \xrightarrow{\text{reciprocal}} \frac{5}{4}$

$-\frac{6}{7} \xrightarrow{\text{reciprocal}} -\frac{7}{6}$

$\frac{1}{2} \xrightarrow{\text{reciprocal}} 2$

$-\frac{1}{3} \xrightarrow{\text{reciprocal}} -3$

$\frac{5}{4} \xrightarrow{\text{reciprocal}} \frac{4}{5}$

$-\frac{7}{6} \xrightarrow{\text{reciprocal}} -\frac{6}{7}$

$a \xrightarrow{\text{reciprocal}}$ and $\frac{b}{c} \xrightarrow{\text{reciprocal}}$

Any number multiplied by its reciprocal is equal to .

Practice

Find the reciprocal of each of the following.

$7$

$\frac{8}{3}$

$-1$

$-\frac{6}{13}$

$2\frac{3}{4}$

$1.25$

$2x$

$\frac{1}{4}x^2$

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

Complete the table for the function $f\left(x\right)=\frac{1}{x}$. Use decimal numbers and round your values to 3 decimal places.
$x$ $-5$ $-4$ $-3$ $-2$ $-1$ $1$ $2$ $3$ $4$ $5$
$f\left(x\right)$
$x$ $-0.5$ $-0.25$ $-0.2$ $-0.1$ $-0.01$ $0$ $0.01$ $0.1$ $0.2$ $0.25$ $0.5$
$f\left(x\right)$


Fill in the table with your values.

Write down the equation of the vertical asymptote.

Write down the equation of the horizontal asymptote.

Draw the graph of $f\left(x\right)=\frac{1}{x}$ in Desmos above.

The domain of $f\left(x\right)=\frac{1}{x}$ is $x\ne$ $, x\in$ .

The range of $f\left(x\right)=\frac{1}{x}$ is $y\ne$ $, y\in$ .