Question

Graph each piecewise function. Then identify the properties.

Answer 1

Domain: (-∞, -2) U [-2, 1] U (1, ∞)

Range: (-∞, 2) U [-3, -∞)

Explanation:

This function is composed of three polynomial functions, a positive slope line
`m = (1)/(2)`, whose domain is all real numbers, a horizontal line, and a negative slope line
`m = -1` whose domain is all real numbers.

Observe in the attached graph that the function has a discontinuity in x = -2, it has a jump.

When x approaches -2 by the left hand, y tends to 2. But when x approaches -2 from the right y tends to -3.

In addition, the function comes from -∞, then has a maximum value at y = 2 and finally derece up to -∞

Then we can conclude that for this piecewise function:

Domain: (-∞, -2) U [-2, 1] U (1, ∞) All Real Numbers

Range: (-∞, 2) U [-3, -∞)