Question - Domain and Range of a Parabolic Function
Solution:
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: $$(-\infty, 5]$$
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