Question

the graph of $f(x)=\frac{4}{x^{2}-2x - 3}$ is shown. for which values of $x$ is $f(x)$ decreasing?

Explanation:

Step1: Analyze the graph

Observe the slope of the curve.

Step2: Identify decreasing intervals

A function is decreasing when the slope of the curve is negative. From the graph, we can see that the function $f(x)=\frac{4}{x^{2}-2x - 3}$ is decreasing on the intervals $(-1,3)$ and $(3,\infty)$.

Answer:

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