Two points on the graph of the linear function f are (0,5) and (3,8). Write a function g whose graph is a reflection in the x-axis of the graph of f.

Step-by-step explanation:

As first step we must obtain the equation of the line. According to Analytical Geometry, we can get a equation of the line by knowing two different points. A linear function is represented by the following expression:

Where:

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

- Slope, dimensionless.

- y-Intercept, dimensionless.

If we know that and , the following system of linear equations is formed:

(Eq. 1)

(Eq. 2)

From (Eq. 1) in (Eq. 2) we get the value of :

The equation of the line that contains the points (0, 5) and (3, 8) is .

As next step we must apply a reflection in the x-axis, whose operation is defined as follows:

That is:

Then, the function is . We plot each function and include the result in the attachment below.