Question

Graph each piecewise function. Then Identify the properties.

Answer 1

Answer:

Shown below

Step-by-step explanation:

A piecewise-defined function is a function defined by two or more equations over a specified domain. From the figure, our piecewise function is:

$\left \{ {{-(x+2)^2+4 \ if \ x \leq 0} \atop {x^2-4x \ if \ x>0}} \right.$

This function has been plotted below and we know some properties:

• The domain is the set of all real numbers

• The range is the set of all real numbers

• The function is the combination of two parabolas

• The point at which the these two parabolas meet is (0,0)

$f(x)=-(x+2)^2+4$ is the parabola in purple while $g(x)=x^2-4x$ is the parabola in orange.