In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3 a. f(-6)

Verified step by step guidance

1. Identify the function: $f(r)=\sqrt{r+6}+3$.
2. Substitute $r=-6$ into the function: $f(-6)=\sqrt{-6+6}+3$.
3. Simplify the expression inside the square root: $\sqrt{0}+3$.
4. Evaluate the square root: $0+3$.
5. Simplify the expression to find the result: $3$.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable into a function to determine its output. In this case, we replace 'r' in the function f(r) = √(r + 6) + 3 with -6 to find f(-6). This process is fundamental in understanding how functions operate and how to compute their values.

Square Root Function

The square root function, denoted as √x, is defined as the value that, when multiplied by itself, gives x. It is important to recognize that the square root function only produces non-negative outputs for non-negative inputs. In the context of the given function, understanding how to handle the square root is crucial for correctly evaluating f(-6).

Simplification

Simplification is the process of reducing an expression to its simplest form. This often involves combining like terms, reducing fractions, or eliminating radicals when possible. After evaluating the function at the specified value, simplifying the result is necessary to present the final answer clearly and concisely.