Domain and Range of a Parabolic Function
The graph shows a parabolic function that opens downwards. The domain represents all the x-values that the function includes, while the range represents all the y-values that the function can attain.
Domain:
The graphed function has endpoints on the x-axis at x = -4 and x = 2, with solid dots at these points indicating that these values are included in the domain. Thus, the domain of the function includes all x-values from -4 to 2.
The domain in interval notation is \([-4, 2]\).
Range:
The highest point on the parabola is at y = 5 (also with a solid dot), which is the maximum value that the function attains, and there are no values higher than this since the parabola opens downward. The lowest y-value appears to extend toward negative infinity as the function will not have a bottom limit within the given domain.
The range in interval notation is \((-\infty, 5]\).
So, the domain and range of the function are:
Domain: \([-4, 2]\)
Range: \((-\infty, 5]\)
