Question

Determine whether each relation defines y as a function of x. Give the domain and range. y=-√x

Accepted Answer

Identify the given relation: $$y = -\sqrt{x}. $$This means $$y is $$defined as the negative square root of $$x. $$Determine the domain by considering the values of $$x$$ for which the expression under the square root is defined. Since the square root function requires the radicand to be non-negative, set $$x \geq 0. $$Check if the relation defines $$y as a $$function of $$x. $$For each $$x in $$the domain, there is exactly one value of $$y$$ because the square root function returns only the principal (non-negative) root, and the negative sign in front makes $$y$$ unique for each $$x. $$Find the range by evaluating the possible values of $$y. $$Since $$y = -\sqrt{x}$$ and $$\sqrt{x} \geq 0$$, $$y$$ will be less than or equal to zero. Thus, the range is $$y \leq 0. $$Summarize: The relation defines $$y as a $$function of $$x$$ with domain $$[0, \infty)$$ and range $$(-\infty, 0].$$

Determine whether each relation defines y as a function of x. Give the domain and range. y=-√x

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Key Concepts

Definition of a Function

Domain of a Function

Range of a Function