Which values are within the range of the piecewise-defined function? f(x) = StartLayout enlarged left-brace 1st Row 1st column 2 x + 2, 2nd column x less-than negative 3 2nd row 1st column x, 2nd column x greater-than negative 3 3rd Row 1st column negative x minus 2, 2nd column x greater-than negative 3 EndLayout y = –6 y = –4 y = –3 y = 0 y = 1 y = 3

A piecewise function is a function that behaves differently in different intervals of its domain. We want to find the range of a given piecewise function and see which ones of the given options are in that range.

We will see that the ones that are in the range are:

y = -6
y = 3

Here our piecewise function is:

f(x) = 2*x + 2 if x < -3
f(x) = -x -2 if x > -3

Now we want to see which values are on the range of this function. Remember that the range of a function is the set of the outputs that we can get of the function.

The range of the first part of the function f(x) = 2*x + 2 has an upper bound at x = -3

f(-3) = 2*-3 + 2 = -6 + 2 = -4

Then the range of the first part is (-∞, -4)

Notice that the actual value -4 does not belong to the range, because x must be smaller than -3.

The range of the second part has a lower bound for x = -3, the lower bound is:

f(-3) = -(-3) - 2 = 1

Then the range of this part is (1, ∞)

Again, 1 is not in the range, as here x must be larger than -3.

Then the range of the piecewise function is:

(-∞, -4) U (1, ∞)

Then, from the given options, the ones that are in the range are:

y = -6

y = 3

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