the graph of $y = f(x)$ is shown below. find all values of $x$ for which $f(x) > 0$.
the graph of $y = f(x)$ is shown below. find all values of $x$ for which $f(x) > 0$.
Answer
Explanation:
Step1: Identify the x - intercepts
The graph intersects the x - axis at (x=-4) and (x = 0).
Step2: Determine the intervals
The intervals to consider are (x<-4), (-4 < x<0), and (x>0).
Step3: Analyze the sign of (y = f(x)) in each interval
- For (x<-4), pick (x=-5). Substitute into the function (by looking at the graph's position). The graph is below the x - axis ((y=f(x)<0)).
- For (-4 < x<0), pick (x=-2). The graph is above the x - axis ((y = f(x)>0)).
- For (x>0), pick (x = 1). The graph is below the x - axis ((y=f(x)<0)).
Answer:
The values of (x) for which (f(x)>0) are (-4 < x<0).