The linear function f(x) = 0.2x + 79 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average test score in your science class, where x is the number of the test taken. x g(x) 1 86 2 84 3 82 Part A: Determine the test average for your math class after completing test 2. (2 points) Part B: Determine the test average for your science class after completing test 2. (2 points) Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points)

The science class had a higher score of 80 as compared to the average score for the math class (79.8)

Step-by-step explanation:

Mathematical Modeling

We are given two linear functions to represent the average test score in the math class and in the science class. The first function f(x) comes as explicit relation between the average test score and the number of the test taken (x):

The second function g(x) shows the relationship with a table from which we can easily give the required results.

A: After completing test 2 (x=2), the average for the math class is

B: After completing test 2, the average for the science class can be found in the table. It results in g(x)=84

C: The average for math class in test 4 is

We cannot determine at simple sight what is the average of the science class after completing test 4. That is one of the limitations of working with tables. We need to find an equation for g(x) as we had on f(x)

To build the function g(x) we need only two points from the table, let's select the first two points (1,86) and (2,84).

The equation of a line, given two points (x1,y1) and (x2,y2) is

Plugging in our values

Operating and making y=g(x)

Now we can find g(4)

It's evident that the science class had a higher score of 80 as compared to the average score for the math class (79.8)