Question

determine the domain on which the following function is decreasing. (a graph is shown with a curve starting at (0,50), peaking around x=3, then decreasing to (8,0).) answer attempt 1 out of 2 input box submit answer buttons: ∅, or, ∪, ∞, <, >, ≤, ≥, ,, ,), (,, (,), all real numbers

Explanation:

Step1: Identify the vertex's x - coordinate

The graph is a parabola - shaped curve (a quadratic - like graph). The vertex (the peak of the curve) is at \(x = 3\) (by looking at the graph, the highest point occurs when \(x = 3\)).

Step2: Determine the interval where the function decreases

A function is decreasing when as \(x\) increases, \(y\) decreases. For this graph, to the right of the vertex (at \(x=3\)) until the end - point of the graph (at \(x = 8\)), the \(y\) - value of the function decreases as \(x\) increases. So the domain on which the function is decreasing is from \(x = 3\) to \(x=8\), including both endpoints since the points at \(x = 3\) (vertex) and \(x = 8\) (the end - point) are part of the function's domain.

Answer:

\([3,8]\)