In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. g(x) = x² - 10x - 3c. g(-x)

Verified step by step guidance

1. Substitute \(-x\) into the function \(g(x) = x^2 - 10x - 3\).
2. The function becomes \(g(-x) = (-x)^2 - 10(-x) - 3\).
3. Simplify \((-x)^2\) to \(x^2\).
4. Simplify \(-10(-x)\) to \(+10x\).
5. Combine the terms to get \(g(-x) = x^2 + 10x - 3\).

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function. In this case, to evaluate g(-x), we replace x in the function g(x) = x² - 10x - 3 with -x. This process allows us to determine the output of the function for that particular input.

Simplification of Expressions

Simplification is the process of reducing an expression to its simplest form. After substituting -x into the function, we will combine like terms and perform any necessary arithmetic operations to simplify the resulting expression. This step is crucial for clearly understanding the behavior of the function.

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form g(x) = ax² + bx + c. The function g(x) = x² - 10x - 3 is a quadratic function where a = 1, b = -10, and c = -3. Understanding the properties of quadratic functions, such as their shape (parabola) and vertex, is essential for analyzing their behavior.