Question

which table represents a nonlinear function?

Explanation:

Step1: Define linear function check

A linear function has a constant rate of change, meaning $\frac{\Delta y}{\Delta x}$ is the same for all pairs of points.

Step2: Check Table 1

Calculate $\frac{\Delta y}{\Delta x}$ for consecutive points:

• $\frac{17-5}{4-2}=\frac{12}{2}=6$
• $\frac{65-17}{8-4}=\frac{48}{4}=12$
• $\frac{101-65}{10-8}=\frac{36}{2}=18$

Rates are not constant.

Step3: Check Table 2

Calculate $\frac{\Delta y}{\Delta x}$ for consecutive points:

• $\frac{12-0}{4-0}=\frac{12}{4}=3$
• $\frac{18-12}{6-4}=\frac{6}{2}=3$
• $\frac{27-18}{9-6}=\frac{9}{3}=3$

Rate is constant (linear).

Step4: Check Table 3

Calculate $\frac{\Delta y}{\Delta x}$ for consecutive points:

• $\frac{-9-(-3)}{5-2}=\frac{-6}{3}=-2$
• $\frac{-13-(-9)}{7-5}=\frac{-4}{2}=-2$
• $\frac{-21-(-13)}{11-7}=\frac{-8}{4}=-2$

Rate is constant (linear).

Step5: Check Table 4

Calculate $\frac{\Delta y}{\Delta x}$ for consecutive points:

• $\frac{5-3}{1-(-1)}=\frac{2}{2}=1$
• $\frac{8-5}{4-1}=\frac{3}{3}=1$
• $\frac{14-8}{10-4}=\frac{6}{6}=1$

Rate is constant (linear).

Answer:

The first table:

x	y
4	17
8	65
10	101