Evaluate each function at the given values of the independent variable and simplify. g(x)=x^2+2

step 1 Let's start by finding the output of negative 1. So wherever we see an X, we're going to replace

Evaluate each function at the given values of the...

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Key Concepts

Algebraic Simplification

Algebraic simplification refers to the process of reducing expressions to their simplest form by performing operations like expanding, combining like terms, and reducing expressions. This technique ensures that the final answer is as clear and straightforward as possible after the substitution has been carried out.

Polynomial Functions

Polynomial functions are expressions consisting of variables raised to whole number powers and their coefficients. In most problems, including this one, understanding how to work with polynomial functions is crucial, as it allows for effective evaluation, manipulation, and simplification through substitution and algebraic expansion.

Function Evaluation

This concept involves replacing the variable in a function with a specified value or expression. By substituting the given value into the function's formula, you can calculate the corresponding output, which is essential when analyzing the behavior of functions at specific points.

Substitution in Functions

Substitution is the process of inserting a particular value or another expression in place of the independent variable within a function. This technique is particularly useful when evaluating functions at modified inputs, such as when the argument is transformed (for example, replacing x with (x+5) or -x).

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