Question

classify this function. the chart has a coordinate grid with a blue graph. options: non - linear, linear

Explanation:

Step1: Recall linear function definition

A linear function's graph is a straight line (or piecewise straight with constant slope segments? Wait, no—linear functions have a constant slope, and their graph is a single straight line. Wait, but this graph is a piecewise function with two line segments, but wait, no—wait, the graph here: let's check the shape. Wait, a linear function has a constant rate of change (slope). But this graph has a peak, so the slope changes. Wait, no—wait, the graph is made of two line segments: from x=-5 to x=-1, it's increasing, and from x=-1 to x=3, it's decreasing. So the slope is positive then negative, so the overall function is not a linear function (since linear functions have constant slope). Wait, but the options are non - linear or linear. Wait, maybe the question is about whether it's a linear function (which requires a single straight line) or non - linear. Wait, the graph is a piecewise function with two linear segments, but as a whole, it's not a linear function (since linear functions are of the form y = mx + b, which is a single straight line). So the function is non - linear.

Step2: Analyze the graph's slope

The left segment (from x=-5 to x=-1) has a positive slope, and the right segment (from x=-1 to x=3) has a negative slope. Since the slope changes (it's not constant throughout the domain), the function does not satisfy the definition of a linear function (which requires a constant slope, i.e., the graph is a single straight line). So the function is non - linear.

Answer:

non - linear