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:

$\left \{ {{\frac{1}{2}(x+1)^2+1 \ if \ x \leq 1} \atop {(x-2)(x-4) \ if \ x>1}} \right.$

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 (1,3)

$f(x)=\frac{1}{2}(x+1)^2+1$ is the parabola in purple while $g(x)=(x-2)(x-4)=x^2-6x+8$ is the parabola in orange.