Question

the graph shows a function. is the function linear or nonlinear?

Explanation:

Step1: Recall linear function definition

A linear function's graph is a straight line (or collinear points), meaning the rate of change (slope) between any two points is constant.

Step2: Check the points' alignment

Visually inspect the plotted points. If we try to draw a line through them, they lie on a straight line (consistent slope). For example, calculate the slope between consecutive points. Let's take two points, say \((x_1,y_1)\) and \((x_2,y_2)\). The slope \(m = \frac{y_2 - y_1}{x_2 - x_1}\) should be constant. From the graph, the points appear collinear, indicating a constant slope.

Answer:

The function is linear.