Question

graph the function.

1. f(x) = (\begin{cases}x + 4 &\text{if } - 7leq x<3\\-4&\text{if }x = 3\\-x + 5&\text{if }x>3end{cases})

Explanation:

Step1: Graph \(y = x + 4\) for \(-7\leq x<3\)

Find two - point on \(y=x + 4\). When \(x=-7\), \(y=-7 + 4=-3\); when \(x = 3\), \(y=3 + 4 = 7\). Draw a line segment from the point \((-7,-3)\) to \((3,7)\) with a closed - circle at \((-7,-3)\) and an open - circle at \((3,7)\).

Step2: Plot the point for \(x = 3\)

When \(x = 3\), \(f(x)=-4\). Plot the point \((3,-4)\) as a closed - circle.

Step3: Graph \(y=-x + 5\) for \(x>3\)

Find a point on \(y=-x + 5\). When \(x = 4\), \(y=-4 + 5 = 1\). Draw a ray starting from the point \((3,2)\) (when \(x = 3\) in \(y=-x + 5\), \(y=2\), but we use an open - circle since \(x>3\)) going to the right.

Answer:

The graph consists of a line segment \(y=x + 4\) for \(-7\leq x<3\) (closed - circle at \((-7,-3)\) and open - circle at \((3,7)\)), a point \((3,-4)\) as a closed - circle, and a ray \(y=-x + 5\) for \(x>3\) (open - circle at \((3,2)\)).