determine the domain on which the following graph of $f(x)$ is negative.
determine the domain on which the following graph of $f(x)$ is negative.
Answer
Explanation:
Step1: Understand when (f(x)) is negative
A function (y = f(x)) is negative when (y=f(x)<0), i.e., the graph of the function lies below the (x -)axis.
Step2: Analyze the graph
Looking at the parabola (quadratic function) graph: The (x -)intercepts (where (y = f(x)=0)) are at (x = 0) and (x=- 2). Since the parabola opens downwards (the coefficient of (x^{2}) is negative, as we can tell from the general shape), the function (y = f(x)) is negative when (x<-2) or (x > 0).
Answer:
((-\infty,-2)\cup(0,\infty))