Final answer:
The range of the function g(x) = -2x + 2 with the domain {x: -3 ≤ x < 2} is all y values such that −4 ≤ y < 0.
Step-by-step explanation:
To find the range of a function based on a given domain, we need to determine the output values of the function when the input values are within the specified domain.
Given the function g(x) = −2x + 2 and the domain {x: −3 ≤ x < 2}, we start by finding the output values at the boundary points of the domain. First, we find g(−3) = −6 + 2 = −4, and then g(2) = −4 + 2 = 0. However, since the function g(x) is a linear function with a negative slope of −2, we know the function is decreasing continuously as x increases within this interval.
Therefore, the range for the given domain is all the values that g(x) takes as x goes from −3 to just below 2. This is the set of all y values such that −4 ≤ y < 0, since −4 is the maximum (occurs at x = −3) and 0 is the value that g(x) approaches but never reaches (since x is less than 2 but not equal to 2).