91Ó°ÊÓ

Use a graphing utility such as Desmos, GeoGebra, or a graphing calculator to plot the function within the given window $$[-4,6] \times[-3,3]$$.

Observe the graph and identify if there are any points at which the function is undefined. Since the denominator has factors of \((y+2)(y-3)\), the function will be undefined when the denominator is equal to zero. That is, the function is undefined at \(y=-2\) and \(y=3\). So, the domain of the function is all real numbers except \(y=-2\) and \(y=3\). In interval notation, the domain can be written as: $$(-\infty, -2) \cup (-2,3) \cup (3, \infty)$$

Since the given window will constrain the values of the function plotted on the graph, we will use the range of the graph within the given window to determine the range of the function. Observe the graph within the range $$[-4,6] \times [-3,3]$$ and identify the minimum and maximum values of the function. The minimum value will occur at the lowest point of the graph within the given window, and the maximum value will occur at the highest point within the window. The range of the function will be all the values between the minimum and maximum values, inclusive of the endpoints if they are within the given window. Based on the graph, you can determine the range of the function within the given window. Let's assume the range is approximately between -2 and 2 (you will need to verify this using the actual graph when you plot the function). In interval notation, the range can be written as: $$[-2,2]$$