Find the domain of the function. \( f(x)=\frac{5}{x+3} \) What is the domain of \( f \) ? A. \( \{x \mid x \) is a real number and \( x \neq 0\} \) B. \( \{x \mid x \) is a real number and \( x \neq-3\} \) C. \( \{x \mid x \) is a real number \( \} \) D. \( \{x \mid x \) is a real number and \( x \neq-3 \) and \( x \neq 0\} \)

To find the domain of the function \( f(x) = \frac{5}{x+3} \), we need to identify values of \( x \) that would make the denominator zero. In this case, \( x + 3 = 0 \) leads us to \( x = -3 \). Therefore, the function is undefined at \( x = -3 \), and the domain consists of all real numbers except \( -3 \). So, the correct choice is B. \( \{x \mid x \) is a real number and \( x \neq -3\} \). Understanding function domains not only helps you avoid errors in calculations but also deepens your overall comprehension of how functions behave. Functions like this one demonstrate the elegance of math, where just one forbidden value can change everything—just don’t let that -3 trip you up! If you're curious about how domains work in other types of functions, check out polynomial, exponential, and logarithmic functions. Each has its quirks! For instance, logarithmic functions can't take negative numbers or zero as input, so always keep an eye out for those tuples that need to be left out of your domain party!