Question

which table represents a nonlinear function?
a.

x	y
2	-9
4	1
6	11

b.

x	y
2	-14
4	-16
6	-18

c.

x	y
2	0
4	6
6	16

Explanation:

Step1: Recall linear function property

A linear function has a constant rate of change, i.e., the slope \( m=\frac{\Delta y}{\Delta x} \) is constant for consecutive \( x - y \) pairs.

Step2: Analyze Option A

For A: \( x: 2, 4, 6 \); \( y: -9, 1, 11 \)
\(\Delta x = 4 - 2 = 2\), \(\Delta y = 1 - (-9)=10\); \(\Delta x = 6 - 4 = 2\), \(\Delta y = 11 - 1 = 10\). Slope \( m=\frac{10}{2}=5 \) (constant). So linear.

Step3: Analyze Option B

For B: \( x: 2, 4, 6 \); \( y: -14, -16, -18 \)
\(\Delta x = 2\), \(\Delta y=-16 - (-14)=-2\); \(\Delta x = 2\), \(\Delta y=-18 - (-16)=-2\). Slope \( m=\frac{-2}{2}=-1 \) (constant). So linear.

Step4: Analyze Option C (assuming C has \( x:2,4,6 \); \( y:0,6,16 \))

\(\Delta x = 2\), \(\Delta y=6 - 0 = 6\); \(\Delta x = 2\), \(\Delta y=16 - 6 = 10\). Slopes \( \frac{6}{2}=3 \) and \( \frac{10}{2}=5 \) (not constant). So nonlinear.

Answer:

C (assuming C is the table with \( x = 2,4,6 \) and \( y = 0,6,16 \))