Question

classify this function. options: non - linear, linear

Explanation:

Step1: Recall linear function definition

A linear function has a constant slope and its graph is a straight line (or piecewise straight with constant slope on each piece? Wait, no—wait, actually, a linear function in the form \(y = mx + b\) is a straight line. But a piecewise function with straight line segments, like an absolute value function (which this resembles, \(y = |x + 1| - 3\) maybe? Wait, no, let's check the graph. Wait, the graph here is made of two straight line segments, but a linear function is a function whose graph is a single straight line. Wait, no—wait, actually, the definition: a linear function is a function that can be written as \(f(x) = mx + b\), where \(m\) and \(b\) are constants, and its graph is a straight line. However, a piecewise function with straight line segments but with a "corner" (like an absolute value function) is a non - linear function? Wait, no, wait. Wait, the absolute value function \(y=|x|\) is a non - linear function? Wait, no, actually, the absolute value function is a piecewise linear function, but in the context of the basic linear vs non - linear classification (especially in basic math, like middle school or early high school), a linear function is a function whose graph is a single straight line (i.e., has a constant slope everywhere). A function with a graph that is not a single straight line (even if it's made of straight line segments but has a "corner" or a change in slope) is non - linear.

Looking at the given graph: it has a "corner" (a point where the slope changes). So the graph is not a single straight line. So it's a non - linear function.

Wait, but let's confirm. The two options are non - linear and linear. A linear function's graph is a straight line (no bends, no corners). This graph has a corner, so it's non - linear.

Step2: Compare with linear function graph

A linear function \(y = mx + b\) has a constant slope. The graph of a linear function is a single straight line. The given graph has two straight line segments meeting at a point (the vertex of the "V" - shape), so it does not represent a single straight line. Therefore, it is a non - linear function.

Answer:

non - linear