Question

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.

Answer 1

Answer:

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:

$y = m\cdot x + b$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$m$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

If we know that $(x_{1}, y_{1}) = (0, 5)$ and $(x_{2}, y_{2}) = (3, 8)$, the following system of linear equations is formed:

$5 = 0\cdot m + b$

$b = 5$ (Eq. 1)

$8 = 3\cdot m + b$

$3\cdot m + b = 8$ (Eq. 2)

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

$3\cdot m + 5 = 8$

$3\cdot m = 3$

$m = 1$

The equation of the line that contains the points (0, 5) and (3, 8) is $f(x) = x + 5$.

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

$(x', y') \longrightarrow (x, -y)$

That is:

$x' = x$

$y' = -y$

Then, the function $g(x)$ is $g(x) = -x-5$. We plot each function and include the result in the attachment below.