Question

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

x	$y=f\left(x\right)$
-2	$\frac{1}{4}$
-1	$\frac{1}{2}$
0	1
1	2
2	4

Short answer

The function is non linear.

Step-by-step solution

Step 1. Given Information 

x	$y=f\left(x\right)$
-2	$\frac{1}{4}$
-1	$\frac{1}{2}$
0	1
1	2
2	4

The data in the table represent values ofy with respect tox.

Compute the average rate of change of each function.

• If the average rate of change is constant, then the function is linear.
• If the average rate of change is not constant, then the function is nonlinear.

Step 2. Calculation 

Calculate average rate of change by the formula $\frac{∆y}{∆x}=\frac{y_2-y_1}{x_2-x_1}$

x	y	$\frac{∆y}{∆x}$
-2	$\frac{1}{4}$	0.25
-1	$\frac{1}{2}$	0.5
0	1	1
1	2	2
2	4

Step 3. Conclusion

The average rate of change is not constant, so the function is not linear.