Question

Graph the following piecewise function.

Answer 1

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:

$x^2+2$

This is a parabola that opens upward and starts at the point $(-5,27)$ and whose vertex is the point $(0,2)$. Keep in mind that $x=-5$ is included in the domain of the function, and we know this by the symbol ≤ that includes the equality.

Second, a linear equation:

$x-4$

The graph of this is a linear function with slope $m=1$ and starts at the point $(3,-1)$. Keep in mind that $x=3$ is included in the domain of the function by the same symbol ≤

Moreover, at $x=3$ there is a jump discontinuity.