Which of the following points is located on the graph of the reciprocal function $$ f(x)=\frac{1}{x} $$ ? (1 poi $$ \left(\frac{1}{21},-21\right) $$ $$ \left(-21,-\frac{1}{21}\right) $$ $$ \left(\frac{5}{7}, \frac{7}{9}\right) $$ $$ \left(\frac{3}{4}, \frac{3}{4}\right) $$

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We need to determine for each point if the $$y$$-coordinate is equal to the reciprocal of the $$x$$-coordinate, that is, if

$$
y = \frac{1}{x}.
$$

1. For the point $$\left(\frac{1}{21}, -21\right)$$:

$$
   \frac{1}{\frac{1}{21}} = 21.
   $$
   
   Since $$21 \neq -21$$, this point is not on the graph.

2. For the point $$\left(-21, -\frac{1}{21}\right)$$:

$$
   \frac{1}{-21} = -\frac{1}{21}.
   $$
   
   This matches the $$y$$-coordinate, so the point is on the graph.

3. For the point $$\left(\frac{5}{7}, \frac{7}{9}\right)$$:

$$
   \frac{1}{\frac{5}{7}} = \frac{7}{5}.
   $$
   
   Since $$\frac{7}{5} \neq \frac{7}{9}$$, this point is not on the graph.

4. For the point $$\left(\frac{3}{4}, \frac{3}{4}\right)$$:

$$
   \frac{1}{\frac{3}{4}} = \frac{4}{3}.
   $$
   
   Since $$\frac{4}{3} \neq \frac{3}{4}$$, this point is not on the graph.

Thus, the correct answer is:

$$
\left(-21, -\frac{1}{21}\right)
$$
The point $$\left(-21, -\frac{1}{21}\right)$$ is on the graph of the reciprocal function $$ f(x) = \frac{1}{x} $$.

Which of the following points is located on the graph of the reciprocal function ? (1 poi

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