Question

for problems 5 and 6, graph the function shown in each table to determine if the function is linear or nonlinear. explain your reasoning. 5 input (x) 0 1 2 output (y) 1 2 5

Explanation:

Step1: Identify coordinate points

Points: $(0,1)$, $(1,2)$, $(2,5)$

Step2: Calculate rate of change

Between $(0,1)$ & $(1,2)$: $\frac{2-1}{1-0}=1$
Between $(1,2)$ & $(2,5)$: $\frac{5-2}{2-1}=3$

Step3: Compare rates of change

$1
eq 3$, so slope is not constant.

Step4: Conclusion

Linear functions have constant slope, so this is non-linear.

Answer:

Non-linear