for the graph: y>x^2+9 what is the range?
To find the range of the graph for the inequality y > x^2 + 9, we need to determine the set of all possible values for the y-coordinate.
Here's how to go about it:
1. Start by understanding the graph of the equation y = x^2 + 9. This is simply a parabola that opens upward. The vertex of the parabola is at the point (0, 9), and it increases indefinitely as x moves away from the vertex in both directions.
2. Now, we consider the inequality y > x^2 + 9. This means that the values of y should be greater than all possible values of x^2 + 9.
3. Notice that the parabola is symmetric around the vertical line x = 0. Since the vertex of the parabola is at (0, 9) and it opens upward, all the points with y-coordinates greater than 9 lie above the parabola.
4. Therefore, the range of the graph for y > x^2 + 9 is all the y-values greater than 9.
In interval notation, the range would be written as (9, +∞), where the "(" indicates that 9 is not included in the range, and "+" denotes that the range extends infinitely in the positive direction.