Question

the graph of f(x) = 1/(x^2 - 4x - 3) is shown. for which values of x is f(x) decreasing?

Explanation:

Step1: Recall decreasing - function property

A function \(y = f(x)\) is decreasing when the slope of the tangent line is negative, i.e., \(f'(x)<0\). Looking at the graph, we observe the intervals where the function is going down as \(x\) increases.

Step2: Analyze the graph

From the graph, we can see that the function \(f(x)\) is decreasing on the intervals \((1,3)\) and \((3,\infty)\).

Answer:

\((1,3)\cup(3,\infty)\)