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Function evaluation involves finding the output of a function given a specific input. For quadratic functions like the one given, this means using the function's formula to calculate the output by plugging in the input value.
For example, in the function \( g(x) = x^2 - 10 \), if we're asked to find \( g(2) \), we substitute 2 into the function.

• First, square the input: \( 2^2 = 4 \).
• Then, perform the subtraction: \( 4 - 10 = -6 \).

As a result, \( g(2) = -6 \). This process helps us see how varying the value of \( x \) affects the output \( g(x) \). Using this method, you can evaluate \( g(x) \) for any input.

The substitution method is a key technique in algebra where we replace a variable with a specific number. This method allows us to find the value of a function for a given input. Let's further explore this method using our example function.
For \( g(2) \), we replace \( x \) with 2 wherever it appears in the equation \( g(x) = x^2 - 10 \).
After substitution, it simplifies to \( 2^2 - 10 \). Similarly, for \( g(3) \), we replace \( x \) with 3, giving us \( 3^2 - 10 \).
The substitution method is particularly useful because it provides a straightforward way to handle functions, regardless of their complexity.
It's essential in solving problems systematically without skipping steps.

Intermediate algebra deals with understanding and manipulating algebraic expressions and functions. It encompasses a variety of concepts, including function evaluation and substitution.
In our example with the function \( g(x) = x^2 - 10 \), we dealt with a quadratic expression, indicative of intermediate algebra.

• Quadratic functions often lead to curved graphs known as parabolas and involve squaring terms.
• By evaluating \( g(2) \) and \( g(3) \), we've performed operations typical in intermediate algebra.

Mastery of substitution and function evaluation in this context allows students to tackle more complex equations. Understanding these concepts builds a foundation for advanced mathematical learning.