Final answer:
To graph the function f(x) = -x + 2 with its domain, plot the line segment between x = -3 (with an open circle) and x = 2 (with a closed circle), slope it downwards, and find the range as (-1, 5).
Step-by-step explanation:
Graphing the Linear Function and Determining Its Range
To graph the function f(x) = -x + 2 with the domain (-3, 2], we start by marking the points on the x-axis where the function will be defined. Since the domain includes numbers greater than -3 and up to and including 2, we will draw a portion of the line that represents the function f(x) starting just right of -3 (due to the open interval) and ending at the point where x = 2. At x = -3, since the domain does not include this point, we will place an open circle to indicate that -3 is not part of the graph. At x = 2, we will put a closed circle to indicate that this point is included.
The line slopes downward because the coefficient of x is negative. To find the range, we look at the y-values that f(x) will take on the given domain. The function decreases as x increases, so at x = -3, the function is not defined exactly at that point but very close to f(-3) = 5. At x = 2, f(2) = 0. Therefore, the range is (-1, 5).