Question

question
graph the following function on the axes provided.
f(x) = { -5x - 11 for x < -1; -1 for x > 4 }

Explanation:

Step1: Analyze first - part of function

For \(y=-5x - 11\) when \(x < - 1\). Find two points on the line. Let \(x=-2\), then \(y=-5\times(-2)-11 = 10 - 11=-1\). Let \(x=-1\), the value of \(y=-5\times(-1)-11=-6\) (but \(x=-1\) is not included in this part of the domain, so we have an open - circle at the point \((-1,-6)\)). Plot the line \(y = - 5x-11\) for \(x < - 1\) with an open - circle at \((-1,-6)\).

Step2: Analyze second - part of function

For \(y = - 1\) when \(x>4\). Let \(x = 5\), \(y=-1\). We have an open - circle at the point \((4,-1)\) since \(x = 4\) is not included in this part of the domain, and then draw a horizontal line \(y=-1\) for \(x>4\).

Answer:

The graph has a line \(y=-5x - 11\) with an open - circle at \((-1,-6)\) for \(x < - 1\) and a horizontal line \(y=-1\) with an open - circle at \((4,-1)\) for \(x>4\).