the graph of $f(x)=\frac{1}{x^{2}-2x - 3}$ is shown. for which values of $x$ is $f(x)$ decreasing?
the graph of $f(x)=\frac{1}{x^{2}-2x - 3}$ is shown. for which values of $x$ is $f(x)$ decreasing?
Answer
Explanation:
Step1: Recall decreasing - function concept
A function $y = f(x)$ is decreasing when, as $x$ increases, $y$ decreases. Looking at the graph of the function $f(x)=\frac{1}{x^{2}-2x - 3}=\frac{1}{(x - 3)(x+1)}$, we can observe its behavior.
Step2: Analyze the graph
From the graph, we can see that as $x$ moves from values greater than 3 towards positive - infinity, the $y$ - values of the function are getting smaller. In the interval $(-1,3)$, the function has two parts (a part above the $x$ - axis and a part below the $x$ - axis) and it is not decreasing throughout this interval. Also, in the intervals involving values less than - 1, the function is not decreasing.
Answer:
C. $(3,\infty)$