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- Maths and statistics
- Functions and graphs
Absolute values turn negative values into positive ones, and leave positive ones unchanged. Absolute value functions are useful for expressing situations where only magnitude matters, without regard to direction, like measuring distance, temperature differences, profit or loss diffeerences, and margin of error. Absolute values The absolute value of any number...
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- Maths and statistics
- Functions and graphs
Circular functions produce periodic wave-like graphs and are foundational in trigonometry. They have broad applications across physics, engineering, and signal processing, where modelling repetitive phenomena and wave patterns is essential. Use this resource to explore circular functions. Circular functions include sine, cosine, and tangent. They describe relationships involving angles and...
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Both the functions y = sin x and y = cos x have a domain of R and a range of [-1,1]. The graphs of both functions have an amplitude of 1 and a period of 2π radians. The functions \(y=\sin x\) and \(y=\cos x\) have a domain of \(\mathbb{R}\)...
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Functions and graphs provide a way to represent, analyse, and understand relationships between different quantities. Use these resources to increase your understanding of functions and graphs. Getting started Plotting points on a graph Use this resource to learn how to plot points on a graph. Relations and functions Use this...
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- Maths and statistics
- Functions and graphs
Simple functions and relations can be transformed into more complicated functions. Seeing how changes in equations affect their visual representation will give you a deeper understanding of functions. This is useful in modelling real-world situations and solving complex maths problems. Use this resource to learn about transformations of graphs. Summary...
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- Maths and statistics
- Hyperbolic functions
The hyperbolic functions are analogous to the circular (trigonometric) functions and are widely used in engineering, science and mathematics. This module introduces hyperbolic functions, their graphs and similarities to the circular functions. Whereas circular functions are defined on a unit circle, the hyperbolic functions are defined on a hyperbola. Hyperbolic...
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- Maths and statistics
- Hyperbolic functions
The differentiation and integration of hyperbolic functions allow us to understand how these functions change and accumulate values which teaches us the essential tools for analysing complex mathematical and real-world systems. Keep reading to learn about these functions and put your new knowledge to the test with some exercises. See...
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- Maths and statistics
- Hyperbolic functions
Providing a function is one to one, it is possible to find an inverse function. This module discusses inverse hyperbolic functions, which are used in advanced calculus for integration and in the solution of differential equations. See Hyperbolic functions for a list of definitions. Inverse hyperbolic functions may also be...
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- Maths and statistics
- Functions and graphs
Hybrid functions combine different types of functions. They are useful for modelling real-world scenarios that have different behaviours under different conditions, like tax brackets or shipping rates. Other examples include analysing frictional forces in physics, designing profiles and shapes for vehicles, and modelling free-fall acceleration. Use this resource to learn...
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Information about functions and graphs to improve your maths skills in these areas. HF1 Hyperbolic functions This module introduces hyperbolic functions, their graphs and similarities to the circular functions. HF2 Derivatives and integrals of hyperbolic functions The hyperbolic functions are widely used in engineering, science and mathematics. HF3 Inverse hyperbolic...
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- Maths and statistics
- Functions and graphs
Interval notation helps to clearly express a continuous range of numbers in a simple, concise way. It is handy in many ways, such as to define acceptable weight limits for a machine, indicating a valid range of measurements in scientific experiments, and specifying temperature ranges in which a machine is...
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- Maths and statistics
- Functions and graphs
One-to-one functions can be inverted so that the inputs and outputs are reversed. They are crucial where we need effective reversal of processes and calculations, like undoing equations in physics, computer graphics transformations, or decrypting data. Use this resource to learn about inverse functions and how to graph them. If...
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- Maths and statistics
- Functions and graphs
Linear functions are the most basic type of function. They are used extensively across STEM and other disciplines, especially to model the rate of physical, biological or economic change. Use this resource to learn about linear functions and graphs. Linear functions create a straight line when graphed. They have the...
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- Maths and statistics
- Functions and graphs
Plotting points on a graph is a foundational skill in maths. Mastering this technique enables you to visualise mathematical relationships and solve equations effectively. Use this resource to get started. The Cartesian plane The Cartesian plane has two perpendicular axes which intersect (cross over) at the origin \(O\). The horizontal...
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- Maths and statistics
- Functions and graphs
Quadratic functions have a distinct parabolic shape. Graphs of quadratic functions have applications in a wide range of fields, like modelling projectile motion, optimising business revenue, analysing population growth and designing bridges and arches. Use this resource to learn about parabolas and how to sketch them. A quadratic function has...
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- Maths and statistics
- Functions and graphs
Understanding relations and functions is crucial for exploring more advanced topics in math and their applications in various scientific and engineering areas. Use this resouce to learn about what functions and relations are. Relations A relation is a set of ordered pairs. For example, \((1,2),(2,6),(3,4),(x,y)\) are ordered pairs. If the...
