Questions: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of f(x) = 3x^2 / (x-7). Find the domain of f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is all real x, except x = . (Type an integer or a decimal. Use a comma to separate answers as needed.) B. The domain is all real x.

Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of f(x) = 3x^2 / (x-7).

Find the domain of f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The domain is all real x, except x = .
(Type an integer or a decimal. Use a comma to separate answers as needed.)
B. The domain is all real x.

Transcript text: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of $f(x)=\frac{3 x^{2}}{x-7}$. Find the domain of $\mathrm{f}(\mathrm{x})$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is all real $x$, except $x=$ $\square$ . (Type an integer or a decimal. Use a comma to separate answers as needed.) B. The domain is all real $x$.

Solution

Solution Steps

Step 1: Determine the Domain of the Function

The function given is $ f(x) = \frac{3x^2}{x-7} $. The domain of a function is the set of all possible input values (x-values) that will not cause the function to be undefined. For rational functions, the denominator cannot be zero. Therefore, we set the denominator equal to zero and solve for $ x $:

\[ x - 7 = 0 \implies x = 7 \]

Thus, the domain of $ f(x) $ is all real numbers except $ x = 7 $.

Final Answer

A. The domain is all real $ x $, except $ x = 7 $.

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