Evaluating a Function
(KS4, Year 10)
The LessonA function is a relation between a set of inputs and a set of outputs, such that each input is related to exactly one output. Evaluating a function means putting an input into a function, and finding the output it relates to.
Understanding Evaluating a FunctionTo evaluate a function means to see what output an input is mapped to. The image below shows a mapping diagram which relates a set of inputs to a set of outputs. If we wanted to evaluate the function when the input is 2, we would see which output it is mapped to.
Imagine we have the function below:
If we evaluate the function at x = 2, we need to find f(2).
A Real Example of How to Evaluate a FunctionEvaluating a function is easy.
QuestionEvaluate the function f(x) = 2x + 1 at x = 2.
Write the function.
f(x) = 2x + 1Note: 2x = 2 × x.
Substitute x = 2 into the function.
f(2) = 2 × 2 + 1 f(2) = 4 + 1 f(2) = 5
Answer:If we evaluate f(x) = 2x + 1 at x = 2, we get 5. f(2) = 5.
Lesson SlidesThe slider below another example of how to evaluate functions. Open the slider in a new tab
A Note on NotationIf a function f is evaluated at a number (e.g. 2), this is denoted f(2).
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