Mathematics, 12.08.2020 04:01 Kaesy24

Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents.

Use the data in the table below, representing both functions, to explain to your boss the solution

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Answer from: jadecharis5339

Given:

Table representing the functions 'f' and 'g'.

f(x) = Number of imports

g(x) = Number of exports

x = Number of months

To find:

Both the functions 'f' and 'g'.Relation between f(x) and g(x)

Solution:

Since, there is a constant increase in the values of function 'f' and 'g', both the functions are the linear functions and the graph of these functions will be a straight line.

Let the equation of the linear function 'f' is,

f(x)=mx+b

Here, = Slope of the line

= y-intercept

Slope of the function 'm' = $\frac{\triangle y}{\triangle x}$

= $\frac{4-3}{2-1}$

= 1

Therefore, equation of the function will be,

f(x)=1(x)+b

f(x)=x+b

Since, this function passes through a point (1,3) ,

f(1)=1+b

3=1+b

b=2

Equation of the function representing the number of imports will be,

f(x)=x+2

Let the equation of the linear function 'g' is,

g(x)=mx+b

Slope of the function (m)= $\frac{\triangle y}{\triangle x}$

$=\frac{3-1}{2-1}$

Therefore, equation of the function 'g' will be,

g(x)=2(x)+b

Since, the function 'g' passes through a point (3,1) ,

g(3)=2(1)+b

1=2+b

b=-1

Therefore, equation of the function representing the exports will be,

g(x)=2x-1

If both the functions have same value,

f(x)=g(x)

x+2=2x-1

2x-x=2+1

x=3

For x=3

f(3)=g(3)=2(3)-1

f(3)=g(3)=5

Therefore, imports and exports of the company are same as in the month of March (x = 3).

Learn more about the linear functions from,

link

Answer from: vargass

Functions are used to show relationship between variables. The system of equations from the table are:

--- for number of imports g(x) = 2x -1

--- for number of exports

The solution in the table represent:

In January, 3 import and 1 exports were madeIn February, 4 imports and 3 exports were madeIn March, 5 imports and 5 exports were madeIn June, 6 import and 7 exports were made

First, we determine the equation of f(x)

Notice that the difference between each entry of f(x) and the next are equal i.e.

6 - 5 = 5 - 4 = 4 - 3 = 1

This means that the function f(x) is linear.

First, we calculate the slope (m) of f(x) as follows:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Considering the entries for months and number of imports, we have:

$(x_1,y_1) =(1,3)\\ (x_2,y_2) =(2,4)$

So, the slope is:

$m = \frac{4 - 3}{2 - 1}$

$m = \frac{1}{1}$

m = 1

The equation is then calculated as:

y = m(x - x_1) + y_1

This gives:

$y = 1 \times (x - 1) + 3$

y = x - 1 + 3

y = x+ 2

Express as a function

f(x) = x+ 2

Hence, the function that represents import is: f(x) = x+ 2

Next, we determine the equation of g(x)

Notice that the difference between each entry of g(x) and the next are also equal i.e. 7 - 5 = 5 - 3 = 3 - 1= 2

This means that the function g(x) is also linear.

Calculate the slope (m) of g(x) as follows:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Considering the entries for months and number of exports, we have:

$(x_1,y_1) =(1,1)\\ (x_2,y_2) =(2,3)$

So, the slope is:

$m = \frac{3 - 1}{2 - 1}$

$m = \frac{2}{1}$

$m = 2\\$

The equation is then calculated as:

y = m(x - x_1) + y_1

This gives:

$y = 2 \times (x - 1) + 1$

y = 2x - 2 + 1

y = 2x -1

Express as a function

g(x) = 2x -1

Hence, the function that represents export is: g(x) = 2x -1

So, the system of equations are:

f(x) = x+ 2 --- for number of imports

g(x) = 2x -1 --- for number of exports

The solution in the table represent:

In January, 3 import and 1 exports were madeIn February, 4 imports and 3 exports were madeIn March, 5 imports and 5 exports were madeIn June, 6 import and 7 exports were made