Find the domain and range of the function \(f(x) = \frac{1}{x+3}\)

Step 1 ：Step 1: Set the denominator equal to zero and solve for \(x\) to find the values that are excluded from the domain. So, \(x + 3 = 0\) which implies \(x = -3\). Thus, the domain of the function is all real numbers except \(-3\). In interval notation, the domain is \((-\infty, -3) \cup (-3, \infty)\).

Step 2 ：Step 2: To find the range, we need to consider the values that \(f(x)\) can take. Since \(f(x)\) is a rational function, it can take any real number value except 0. Thus, the range of the function is all real numbers except 0. In interval notation, the range is \((-\infty, 0) \cup (0, \infty)\).