Answer:
(a) g(-4) = 3, g(-2) = 2, g(0) = -2, g(2) = 1, g(4) = 0
(b) Domain: [-4, 4]
Range: [-2. 3]
Step-by-step explanation:
The given graph is the graph of a piecewise function.
In the graph of a piecewise function:
- An open circle at an endpoint indicates that the value is not included in the interval of this piece of the function.
- An closed circle at an endpoint indicates that the value is included in the interval of this piece of the function.
Part (a)
To find g(-4), g(-2), g(0), g(2) and g(4), locate the corresponding y-coordinates for the points on the graph where the x-coordinates are -4, -2, 0, 2 and 4 respectively:
[tex]g(-4) = 3\\\\g(-2) = 2\\\\g(0) = -2\\\\g(2) = 1\\\\g(4) = 0[/tex]
Part (b)
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
To find the domain of a piecewise function, begin by identifying the domain of each piece of the function, which is [-4, 2] and (2, 4]. Now, combine these intervals, which results in the overall domain being [-4, 4].
The range of a function is the set of all possible output values (y-values) for which the function is defined.
To find the range of a piecewise function, begin by identifying the range of each piece of the function, which is [-2, 3] and [0, 3). Now, combine these intervals, which results in the overall range being [-2. 3].
