Question

Graph the following piecewise function.

Answer 1

Shown below

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.