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Chapter 1: Problem 15

Graph each function with a graphing utility using the given window. Then state the domain and range of the function. $$f(x)=\sqrt{4-x^{2}} ; \quad[-4,4] \times[-4,4]$$

Short Answer

Expert verified
Question: Determine the domain and range of the function $$f(x) = \sqrt{4-x^2}$$ when graphed within the window $$[-4,4] \times[-4,4]$$. Answer: The domain is $$x 鈭� [-2, 2]$$, and the range is $$f(x) 鈭� [0, 2]$$.

Step by step solution

01

Graph the function in a graphing utility

Use a graphing utility like Desmos or Grapher to plot the given function within the window $$[-4,4] \times[-4,4]$$. You will get a graph of the function $$f(x) = \sqrt{4-x^2}$$.
02

Identify the domain

The domain of a function represents all possible values of x for which the function is defined. In this case, looking at the graph we can see that the function is defined for all values of x within the interval $$[-2, 2]$$. Thus, the domain is $$x 鈭� [-2, 2]$$.
03

Identify the range

The range of a function represents all possible values of f(x) for which the function is defined. From the graph, we can observe that the function's values cover all the values of f(x) within the interval $$[0, 2]$$. Thus, the range is $$f(x) 鈭� [0, 2]$$. The graph of the function $$f(x)=\sqrt{4-x^{2}}$$ within the window $$[-4,4] \times[-4,4]$$ is shown. The domain of the function is $$x 鈭� [-2, 2]$$, and its range is $$f(x) 鈭� [0, 2]$$.

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