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Evaluating functions is a fundamental concept in mathematics. It involves determining the output value of a function for a specific input value. To evaluate a function, you need to know the rule of the function and then substitute the given input into this rule. For example, in the given exercise, the function is defined as \(k(x) = 9\). Here, evaluating the function at \(x = 200\) means finding the value of the function when \x\ is 200.
Always remember to substitute the input value into the function and perform any arithmetic operations needed.

For constant functions like \(k(x) = 9\), the output remains the same no matter what the input value is. Thus, \(k(200) = 9\) because the function always outputs 9.
This process simplifies significantly in the case of constant functions.

In general:

• Identify the rule of the function.
• Substitute the given input value into the function.
• Perform any necessary arithmetic operations to find the result.

Function notation is a way to clearly define and communicate how a function operates. In function notation, functions are typically written as \(f(x)\) where \(f\) is the name of the function and \(x\) is the variable. For example, in the exercise, the function \(k(x) = 9\) tells us that regardless of the value of \(x\), the function \(k\) produces 9.
It's important to note that the variable name \(x\) is simply a placeholder and can be replaced with any symbol. The function will still behave the same way.

Function notation makes it easy to specify the particular function you are working with and the specific input value. This is particularly helpful in more complicated functions where multiple variables and operations are involved.

Remember:

• \k(x)\ specifies the name of the function and its variable.
• \k(200)\ tells us to evaluate the function for the input value of 200.
• The output correctly follows from the stated rule of the function.

Use notation clearly to communicate exact operations performed by the function.

Algebraic evaluation involves substituting the variable in a function with a given number and performing the necessary arithmetic operations to determine the output. In the case of the given problem, the function \(k(x) = 9\) is a constant function. This means that no matter what value you substitute for \x\, the result is always 9.
To evaluate \k(200)\:

Identify that \k(x) = 9\ is a constant function.

The output is directly given by the constant value which is 9.

Thus, \k(200) = 9\ without the need for further arithmetic operations.

Constant functions are among the simplest types of functions to evaluate because the output remains unchanged for any input.
In summary:

• The main step is substitution.
• For constant functions, recognize that the output does not depend on the input value.
• This makes the evaluation straightforward and quick.

This simplicity helps to reinforce your understanding of more complex function evaluations when other types of functions are involved.