Decide whether the function is one-to-one. \( y=\frac{-3}{x+9} \) Is the function one-to-one? Yes No

To determine if the function \( y=\frac{-3}{x+9} \) is one-to-one, we can use the horizontal line test. A function is one-to-one if every horizontal line intersects the graph at most once. For this rational function, as \( x \) approaches negative infinity, \( y \) approaches 0, and as \( x \) approaches negative 9, \( y \) approaches negative infinity. Because the function is always decreasing and passes the horizontal line test, it is indeed one-to-one! Another way to check if a function is one-to-one is by calculating its derivative. If the derivative does not change sign (i.e., is always positive or always negative), then the function is one-to-one. For this function, the derivative is negative, confirming the function is decreasing throughout its domain, further solidifying that it is one-to-one.