the graph of $f(x)=\frac{4}{x^{2}-2x - 3}$ is shown. for which values of $x$ is $f(x)$ decreasing?
the graph of $f(x)=\frac{4}{x^{2}-2x - 3}$ is shown. for which values of $x$ is $f(x)$ decreasing?
Answer
Explanation:
Step1: Recall decreasing - function property
A function $y = f(x)$ is decreasing when the slope of the tangent line is negative, i.e., $f'(x)<0$. We can also determine from the graph.
Step2: Analyze the graph
Looking at the graph of $y = f(x)=\frac{4}{x^{2}-2x - 3}=\frac{4}{(x - 3)(x+1)}$, we observe the intervals where the graph is going down - ward as we move from left to right. The function is decreasing on the intervals $(-\infty,-1)$ and $(1,3)$.
Answer:
$x\in(-\infty,-1)\cup(1,3)$