Evaluating a function means determining the value of the function, usually denoted as f(x) or y, for a specific value of x. In simpler terms, you're finding the "output" of the function for a given "input".
Here's a breakdown of the process:
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Understand the Function Notation: A function is typically written as f(x) = [expression], where:
- f is the name of the function.
- x is the input variable.
- [expression] is the rule that defines how the input x is transformed to produce the output.
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Identify the Input Value: The problem will provide you with a specific value for x that you need to evaluate. For example, you might be asked to evaluate f(2). This means you need to find the value of the function when x = 2.
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Substitute: Replace every instance of the variable x in the function's expression with the given input value.
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Simplify: Perform the necessary mathematical operations (addition, subtraction, multiplication, division, exponents, etc.) according to the order of operations (PEMDAS/BODMAS) to simplify the expression and obtain a numerical value.
Example:
Let's say you have the function f(x) = 3x + 2. You want to evaluate f(4).
- Input Value: x = 4
- Substitute: f(4) = 3(4) + 2
- Simplify: f(4) = 12 + 2 = 14
Therefore, f(4) = 14.
Another Example:
Consider the function g(x) = x2 - 5x + 6. Evaluate g(-1).
- Input Value: x = -1
- Substitute: g(-1) = (-1)2 - 5(-1) + 6
- Simplify: g(-1) = 1 + 5 + 6 = 12
Therefore, g(-1) = 12.
In essence, evaluating functions is about substituting a given value for the input variable and simplifying the resulting expression to find the corresponding output.
