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Chapter 3: Problem 48

Give the domain and the range of each quadratic function whose graph is described. Minimum \(=18\) at \(x=-6\)

Short Answer

Expert verified
The domain of the function is \(-\infty < x < \infty \) and the range is \(y \geq 18\).

Step by step solution

01

Identify the Domain

The domain of a function includes all possible x-values, or inputs. For any quadratic function, there are no restrictions on x, so the domain will be all real numbers, represented as \(-\infty < x < \infty \).
02

Identify the Range

The range of a function includes the set of all possible output values (y-values). Here, we are given that the minimum y-value is 18. Because the function is a parabola that opens upward, the y-values will include 18 and every number larger than 18. So, the range is \(y \geq 18\).

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