Question

q. what is the range of the following graph? (graph with points (-4,1), (-2,-1), (0,-5), (3,5), (6,0))

Explanation:

Step1: Identify y - coordinates

List the y - coordinates of all the points: For \((3,5)\), y - coordinate is \(5\); for \((-4,1)\), y - coordinate is \(1\); for \((6,0)\), y - coordinate is \(0\); for \((-2,-1)\), y - coordinate is \(-1\); for \((0,-5)\), y - coordinate is \(-5\).

Step2: Determine the range

The range of a set of points is the set of all y - values. Find the minimum and maximum y - values. The y - values are \(-5\), \(-1\), \(0\), \(1\), \(5\). The minimum y - value is \(-5\) and the maximum is \(5\). So the range is all real numbers from \(-5\) to \(5\), or in set notation \(\{-5, - 1,0,1,5\}\) (since these are discrete points, the range is the set of these y - values). But if we consider the range as the set of all y - coordinates of the given points, we list them.

Answer:

The range of the graph (set of y - coordinates of the points) is \(\{-5, - 1,0,1,5\}\) (or in interval notation, since the points are discrete, but if we consider the possible y - values from the minimum \(-5\) to maximum \(5\) among these points, the range is \(\{-5, - 1,0,1,5\}\)).