Question

The function f(x) is shown in the graph.

Answer 1

Answer: $f(x)=-\frac{3}{4}x-3$

This is a graph of a Line, the equation of a line is in the following form:

$y=f(x)=mx+b$   (1)

Where:

$m$ is the slope of the line

$b$ is the point of intersection of the line with the y-axis

Now, in order to write the equation (1), we have to find the slope first by the following formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$    (2)

Where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points of the line.

In this case:

$(x_{1},y_{1})=(-4,0)$

$(x_{2},y_{2})=(0,-3)$

Substituting:

$m=\frac{-3-0}{0-(-4)}$    (3)

$m=-\frac{3}{4}$    (4) >>>>This is the slope

Now we have to find the interception with the y-axis, if we look at the graph we will find out the line intercepts with the y-axis in y=-3.

Therefore $b=-3$   (5)

Finally we can write the function:

$f(x)=-\frac{3}{4}x-3$