Question

use the graph to answer the question. which of the following functions is represented by the graph? (1 point) power; $y = x^n$ reciprocal; $y = \frac{1}{x}$ exponential; $y = b^x$ absolute value; $y = |x|$

Explanation:

1. A power function $y=x^n$ has a different shape (e.g., parabola for $n=2$, line for $n=1$) and does not have two separate branches in opposite quadrants like the given graph.
2. The reciprocal function $y=\frac{1}{x}$ has two hyperbolic branches: one in the first quadrant (positive $x$, positive $y$) and one in the third quadrant (negative $x$, negative $y$), which matches the graph exactly.
3. An exponential function $y=b^x$ is only defined for positive $y$-values (when $b>0$) and does not have a branch in the third quadrant.
4. The absolute value function $y=|x|$ forms a V-shape and is defined for all $x$ with non-negative $y$-values, which does not match the graph.

Answer:

reciprocal; $y=\frac{1}{x}$