Answer:
[tex]\displaystyle f(x)=\left \{ {{y=5 \text{ for } x < 0} \atop {4x - 6 \text{ for } -4 \leq x \leq 4}} \right.[/tex]
Step-by-step explanation:
The rule that defines a piecewise-defined function is the different equations and functions that make up the given piecewise-defined function. Based on the graph, we will have two equations. Let the piecewise function be defined as f(x).
The left piece is a horizontal line, so we will have a y = equation.
The right piece can be written in slope-intercept form, which becomes y = 4x - 6. Pay attention to the scale of the y-axis as it is different from the scale of the x-axis.
Since the left piece has an open circle, we will use <, and the right piece will use ≤ to define this point.
Altogether, this gives us the rule:
[tex]\displaystyle f(x)=\left \{ {{y=5 \text{ for } x < 0} \atop {4x - 6 \text{ for } -4 \leq x \leq 4}} \right.[/tex]
