Question

problems 8 - 11, in each data sets below, state the type of model that best represents the data and give an explanation to justify why the model fits. 8.

x	1.2	3	4.8	6.6	8.4
f(x)	2.2	3.1	4	4.9	5.8

9.

x	-3	-2	-1	0	1
f(x)	-2	-5	-6	-5	-2

Explanation:

Problem 8

Step1: Calculate differences in x - values

$3 - 1.2=1.8$, $4.8 - 3 = 1.8$, $6.6 - 4.8=1.8$, $8.4 - 6.6 = 1.8$

Step2: Calculate differences in f(x) - values

$3.1 - 2.2 = 0.9$, $4 - 3.1=0.9$, $4.9 - 4 = 0.9$, $5.8 - 4.9 = 0.9$

Step3: Determine the model type

Since the differences in x - values are constant ($\Delta x=1.8$) and the differences in f(x) - values are constant ($\Delta f(x)=0.9$), the data follows a linear model.

Step1: Observe symmetry

Notice that when $x=-3,f(x)=-2$ and when $x = 1,f(x)=-2$; when $x=-2,f(x)=-5$ and when $x = 0,f(x)=-5$.

Step2: Determine the model type

The data is symmetric about the line $x=-1$. A quadratic function has a parabolic shape which is symmetric about its axis of symmetry. So, the data follows a quadratic model.

Answer:

The model is linear. The constant first - order differences in both x and f(x) values justify this.

Problem 9