Answer:
Shown below
Step-by-step explanation:
A piecewise function is a function defined by two or more equations. In this problem, we have a function defined by two equations.
First, a quadratic equation:
[tex]x^2+2[/tex]
This is a parabola that opens upward and starts at the point [tex](-5,27)[/tex] and whose vertex is the point [tex](0,2)[/tex]. Keep in mind that [tex]x=-5[/tex] is included in the domain of the function, and we know this by the symbol ≤ that includes the equality.
Second, a linear equation:
[tex]x-4[/tex]
The graph of this is a linear function with slope [tex]m=1[/tex] and starts at the point [tex](3,-1)[/tex]. Keep in mind that [tex]x=3[/tex] is included in the domain of the function by the same symbol ≤
Moreover, at [tex]x=3[/tex] there is a jump discontinuity.
