Question

determine the domain on which the following function is decreasing.

Explanation:

Step1: Recall the definition of a decreasing function

A function \(y = f(x)\) is decreasing on an interval if for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze the given graph

Looking at the parabola (quadratic function) graph:

• We observe the direction of the graph. The graph of the function is a parabola opening upwards (since it has a minimum point).
• For a parabola \(y = ax^{2}+bx + c\) (\(a>0\)), the function is decreasing to the left of the vertex and increasing to the right of the vertex.
• The vertex of the parabola (the point where the function changes from decreasing to increasing) has an \(x\) - coordinate of \(x = 3\).
• As \(x\) moves from \(-\infty\) to \(3\), if we take two points \(x_1

Answer:

The function is decreasing on the interval \((-\infty,3)\)