Question

Graph each piecewise function. Then identify the properties.

Answer 1

Domain: (-∞, 0] U (0, ∞): All real numbers.

Range: (-∞, ∞)

Explanation:

This function is composed of two polynomial functions, a quadratic whose domain is all real numbers and a negative slope whose domain is all real numbers.

Observe in the attached graph that the function is continuous for the whole domain, it does not have any jump. In addition, the parabolic function comes from ∞, then it has a minimum value in y = 1 it grows up to y = 4. Finally it joins with the equation of the line and it extends to -∞.

Then we can conclude that for this piecewise function:

Domain: (-∞, 0] U (0, ∞): All real numbers.

Range: (-∞, ∞)