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What is a Function?
What is a Function?
A simple way to think of a function is that it is a machine that processes an input into a single output. We can write this as:
A simple way to think of a function is that it is a machine that processes an input into a single output. We can write this as:
f (a) = b
f (a) = b
where f is the function, a is the input and b is the output.
where f is the function, a is the input and b is the output.
Note that f is a special notation and not an algebraic term.
Note that f is a special notation and not an algebraic term.
In Sec 1, we learnt about linear equations and graphs as y = mx + c. An example of linear function looks like:
In Sec 1, we learnt about linear equations and graphs as y = mx + c. An example of linear function looks like:
f (x) = 3x + 2
f (x) = 3x + 2
If we set the input to 5, we can evaluate the function
If we set the input to 5, we can evaluate the function
f (5) = 3(5) + 2 = 17
f (5) = 3(5) + 2 = 17
giving us an output of 17.
giving us an output of 17.
Try it.
Try it.
Given that f (x) = 3x + 1, compute f (5) and f (0).
Given that f (x) = 3x + 1, compute f (5) and f (0).
Answers
Answers
f (5) = 3(5) + 1 = 16
f (5) = 3(5) + 1 = 16
f (0) = 3(0) + 1 = 1
f (0) = 3(0) + 1 = 1
Types of Functions
Types of Functions
In Additional Mathematics, we are going to cover many new types of functions. We will start by reviewing (and expanding on) quadratic functions and deepening what you have learnt in Elementary Mathematics then moving on to:
In Additional Mathematics, we are going to cover many new types of functions. We will start by reviewing (and expanding on) quadratic functions and deepening what you have learnt in Elementary Mathematics then moving on to:
- Surd Functions
- Exponential Functions
- Logarithmic Functions
- Polynomial Functions
- Trigonometric Functions
Computational Thinking Example (Function)
Computational Thinking Example (Function)
Click on the diagram to go to a Python Script to compute a patient's Ideal Weight.
Click on the diagram to go to a Python Script to compute a patient's Ideal Weight.
This function computes the ideal weight using the BMI formula:
This function computes the ideal weight using the BMI formula:
Ideal Weight = f(Height) = BMI * Height (m) * Height (m)
Ideal Weight = f(Height) = BMI * Height (m) * Height (m)
The input is the patient's height and the output is the patient's ideal weight.
The input is the patient's height and the output is the patient's ideal weight.
The Under Function computes the lower bound of the ideal weight using a BMI of 18.5 while the Over Function computes the upper bound of the ideal weight using a BMI of 23.
The Under Function computes the lower bound of the ideal weight using a BMI of 18.5 while the Over Function computes the upper bound of the ideal weight using a BMI of 23.
Extend!
Extend!
Learn more about functions in this video below.
Learn more about functions in this video below.
Next Page: Quadratic Functions
Next Page: Quadratic Functions
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