determine the domain on which the following graph of $f(x)$ is positive.
determine the domain on which the following graph of $f(x)$ is positive.
Answer
Explanation:
Step1: Understand the graph
The graph of a function (y = f(x)) is positive when (y>0), i.e., the part of the graph above the (x -)axis.
Step2: Identify the (x -)intercepts
The (x -)intercepts of the graph (where (y = 0)) are at (x=-1) and (x = 7).
Step3: Determine the interval
For a parabola opening downwards (since the coefficient of (x^{2}) is negative, as we can tell from the shape), the function (y=f(x)) is positive between the two (x -)intercepts.
Answer:
The domain on which (f(x)) is positive is (-1<x<7) or in interval notation ((-1,7))