BeginnerTopic 12 of 104Engineering Mathematics
Functions and graphs
A function maps each input to one output; graphs reveal trends, intercepts and asymptotes.
In depth
A function assigns exactly one output to each input. Its domain is the allowed inputs and range the outputs. Graphs show intercepts, growth, symmetry and asymptotes. Transformations shift, stretch or reflect a graph: f(x-a)+b moves it right a and up b.
Key points
- Vertical line test identifies functions
- Composition f(g(x)) chains functions
- Inverse functions undo each other
ExampleThe stopping distance d=v²/(2μg) is a quadratic function of speed.
A function describes how one quantity depends on another, and graphs reveal trends, limits and asymptotes at a glance.
What is Functions and graphs?
A function maps each input to one output; graphs reveal trends, intercepts and asymptotes.
Why is it important to understand functions and graphs?
A function describes how one quantity depends on another, and graphs reveal trends, limits and asymptotes at a glance.
What is the difference between a function and a relation?
A function gives exactly one output for each input. A circle is a relation but not a function of x, because a vertical line meets it twice.
How do I find an asymptote?
Look for values where the denominator is zero, and check the behaviour of the function as x grows large in either direction.
How is Functions and graphs used in practice?
Typical applications include plotting a pump characteristic curve, reading a stress-strain curve to find yield strength and describing how cost falls as production volume rises.
What should I learn before Functions and graphs?
Study "Inequalities" first (topic 11 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Functions and graphs?
Vertical line test identifies functions. Composition f(g(x)) chains functions. Inverse functions undo each other.
Can you give an example of Functions and graphs?
The stopping distance d=v²/(2μg) is a quadratic function of speed.
What comes after Functions and graphs?
The next topic is "Trigonometry basics", which builds directly on this one.
How difficult is Functions and graphs?
It is classed as Beginner in Engineering Mathematics (topic 12 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.