Question

which function is represented by this graph?
a. $f(x) = \frac{x}{3}$
b. $f(x) = \frac{x}{6}$
c. $f(x) = \frac{3}{x}$
d. $f(x) = \frac{6}{x}$

Explanation:

Step1: Identify function type

This is a reciprocal function $f(x)=\frac{k}{x}$ with two hyperbola branches in Quadrants I and III.

Step2: Verify $k$ with a point

Use the point $x=2$, $y=3$ from the graph:
$3=\frac{k}{2} \implies k=6$

Answer:

D. $f(x)=\frac{6}{x}$