Question

from memory match the equation with its graph. \\( f(x) = \frac{1}{x} \\) try again

Explanation:

The function $f(x)=\frac{1}{x}$ is a reciprocal function. It has two hyperbola branches: one in the first quadrant (where $x>0$, $y>0$) and one in the third quadrant (where $x<0$, $y<0$). It is undefined at $x=0$, so there is a vertical asymptote at $x=0$, and a horizontal asymptote at $y=0$. Graph A is an absolute value function, Graph C is a one-branch curve, while Graph B matches the shape and quadrants of $f(x)=\frac{1}{x}$.

Answer:

B. The graph with two hyperbola branches in the first and third quadrants