Questions: Graph and state the domain. y=9/x^2 The domain is (Type your answer in interval notation.)

Graph and state the domain. y=9/x^2 The domain is (Type your answer in interval notation.)
Transcript text: Graph and state the domain. \[ y=\frac{9}{x^{2}} \] The domain is $\square$ (Type your answer in interval notation.)
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Solution

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Solution Steps

Step 1: Analyze the function

The given function is y = 9/x². This represents a rational function where the numerator is a constant and the denominator is x².

Step 2: Determine the graph

The graph of this function will have vertical asymptotes where the denominator is zero, which occurs at x = 0. Since the numerator is positive and the denominator is always positive (except at x=0), the graph will exist entirely above the x-axis. The correct graph is C.

Step 3: Find the domain

The domain of the function is all real numbers except where the denominator is equal to zero. In this case, x² is equal to zero only when x = 0. Therefore, the domain is all real numbers except x = 0.

Final Answer

The graph is C, and the domain is (-∞, 0) U (0, ∞).

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