What is the domain of the given function below? \( f(x)=\frac{x-4}{x-3} \) All \( x \)-values except \( x=4 \) All \( x \)-values except \( x=-4 \) and \( x=3 \) All \( x \)-values except \( x=-4 \) All \( x \)-values except \( x=3 \)

The function \( f(x) = \frac{x-4}{x-3} \) is defined for all \( x \) except where the denominator equals zero. In this case, the denominator \( x - 3 = 0 \) gives us the point \( x = 3 \). Hence, the domain includes all real numbers except \( x = 3 \). Understanding the concept of function domain is like being a detective! You're looking for where the function can "safely function." Just as crossing a street can be dangerous when the light is red, some values in algebra can cause a function to misbehave - specifically, division by zero! Always keep an eye out for those trouble spots. If you want to explore further, look into rational functions and their properties. A great book on the topic is "Understanding Algebraic Expressions" by Robert Lang. It delves into the world of functions, domains, and those sneaky undefined values that can trip you up! It’s a perfect read to enhance your math skills and get a grip on these fundamental concepts.