Question

Evaluate $g(-x), g(2 x),$ and $g(a+h)$. $$g(x)=-x^{2}-3 x+5$$

   Evaluate $g(-x), g(2 x),$ and $g(a+h)$.
$$g(x)=-x^{2}-3 x+5$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 1, Problem 31

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Solved by Expert Charles Carter

05/05/2020

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Evaluate $g(-x), g(2 x),$ and $g(a+h)$. $$g(x)=-x^{2}-3 x+5$$

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Key Concepts

Function Evaluation and Substitution

This concept involves replacing the variable in a function with another expression. When evaluating a function at a different input, you substitute the new value or expression into the function’s formula and then simplify the result.

Polynomial Functions

A polynomial function consists of terms with non-negative integer exponents. Understanding the structure of polynomial functions is crucial, as it allows you to perform substitutions and apply exponent rules correctly to obtain the new simplified expression.

Algebraic Simplification

After substituting a new expression into a function, algebraic simplification techniques are employed. This includes expanding squared expressions, distributing multiplication over addition, and combining like terms to achieve a concise and simplified form.

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