In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.g(x) = x² + 2x + 3 a. g(-1)

Verified step by step guidance

1. Substitute the given value of the independent variable, x = -1, into the function g(x) = x² + 2x + 3. This means replacing every instance of x in the function with -1.
2. Write the substituted expression: g(-1) = (-1)² + 2(-1) + 3.
3. Simplify the first term: (-1)² = 1.
4. Simplify the second term: 2(-1) = -2.
5. Combine all the terms: g(-1) = 1 - 2 + 3. Simplify further to get the final result.

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function to find the corresponding output. In this case, we replace 'x' in the function g(x) = x² + 2x + 3 with -1 to determine g(-1). This process is fundamental in understanding how functions operate and how to compute their values.

Polynomial Functions

The function g(x) = x² + 2x + 3 is a polynomial function, specifically a quadratic function because its highest degree is 2. Polynomial functions are composed of variables raised to whole number powers and can be analyzed for their behavior, roots, and graphing characteristics. Understanding the structure of polynomial functions is essential for evaluating them.

Simplification

Simplification refers to the process of reducing an expression to its simplest form. After evaluating the function g(-1), the resulting expression may need to be simplified by combining like terms or performing arithmetic operations. This step is crucial for presenting the final answer clearly and concisely.