Questions: Given the graph, find the following: Domain: Range: x-intercept(s): y-intercept: End Behaviors: Vertex: Increasing Interval(s): Decreasing Interval(s):

Solution Steps

The domain of a graph is the set of all possible x-values. Since the graph extends infinitely to the left and right, the domain is all real numbers.

The range of a graph is the set of all possible y-values. The lowest point on the graph is at y = -3, and the graph extends infinitely upwards. Therefore, the range is \([-3, \infty)\).

The x-intercepts are the points where the graph crosses the x-axis. This occurs at x = -3 and x = 1.

The y-intercept is the point where the graph crosses the y-axis. This occurs at y = -1.

As x approaches negative infinity, y approaches positive infinity. As x approaches positive infinity, y approaches positive infinity.

The vertex is the lowest point on the parabola. In this case, the vertex is at (-1, -3).

The graph is increasing from x = -1 to positive infinity. So the increasing interval is \((-1, \infty)\).

The graph is decreasing from negative infinity to x = -1. So the decreasing interval is \((-\infty, -1)\).

Final Answer