(2) Introduction to functions
This lesson covers:
- What a function is
- How to evaluate a function
What is a function?
A function takes an input and produces an output. They do this by following a specific rule.
The rule is defined by the function's equation.
For example, the equation f(x) = 5x + 2 means that the function f takes a value for (x), multiplies it by 5, and then adds 2.
Evaluating functions
To evaluate a function means to find the output for a given input by substituting the input value into the function's formula.
The function machine below has the function f(x) = 2x + 7.
To evaluate this function for specific values of x, simply replace (x) with the given value and calculate the result.
How to calculate the output value:
- Write out the equation for the function.
- Substitute the input: replace the x in the function's formula with the value you're evaluating.
- Perform the calculations and record the output value.
For (x = 3):
f(x) = 2x + 7
f(3) = 2(3) + 7 = 6 + 7 = 13
For (x = -2):
f(x) = 2x + 7
f(-2) = 2(-2) + 7 = -4 + 7 = 3
Worked example 1: Evaluating functions
A function has the equation f(x) = 10x + 15.
Calculate the value of f(x) when x = 2.
Worked example 2: Evaluating functions
A function has the equation f(x) = -6x + 13.
Calculate the value of f(x) when x = -3.
Worked example 3: Evaluating functions
A function has the equation f(x) = x2 + 4x - 5.
Calculate the value of f(x) when x = 2.
A function has the equation f(x) = 7x + 12.
Calculate the value of f(x) when x = -3.
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A function has the equation f(x) = 4x - 8.
Calculate the value of f(x) when x = 2.
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A function has the equation f(x) = x2 - 3x + 6.
Calculate the value of f(x) when x = -3.
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A function has the equation f(x) = x2 + 2x - 16.
Calculate the value of f(x) when x = 4.
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