Question

graph the following function on the axes provided.
f(x)=\begin{cases}-4&\text{for }x < - 5\\4x - 15&\text{for }x>3end{cases}
click and drag to make a line. click the line to delete it. click on an endpoint of a line to change it.

Explanation:

Step1: Graph \(y = - 4\) for \(x < - 5\)

For the part \(y=-4\) when \(x < - 5\), we draw a horizontal line at \(y = - 4\). Since \(x=-5\) is not included, we use an open - circle at the point \((-5,-4)\) and the line extends to the left.

Step2: Graph \(y = 4x-15\) for \(x>3\)

First, find the \(y\) - value when \(x = 3\) for the line \(y = 4x-15\). Substitute \(x = 3\) into \(y=4x - 15\), we get \(y=4\times3-15=-3\). Since \(x = 3\) is not included for \(y = 4x-15\), we use an open - circle at the point \((3,-3)\).
The slope of the line \(y = 4x-15\) is \(m = 4\) and the \(y\) - intercept is \(b=-15\). We can find another point, for example, when \(x = 4\), \(y=4\times4-15=1\). Then we draw a line with slope \(4\) starting from the open - circle at \((3,-3)\) and extending to the right.

Answer:

Graph a horizontal line \(y = - 4\) with an open - circle at \((-5,-4)\) extending to the left and a line \(y = 4x-15\) with an open - circle at \((3,-3)\) and slope \(4\) extending to the right.