![]() ![]() In either notation, you do exactly the same thing: you plug −1 in for x, multiply by the 2, and then add in the 3, simplifying to get a final value of 1.īut function notation gives you greater flexibility than using just " y" for every formula. Now you say " f ( x) = 2 x 3 find f (−1)" (pronounced as " f-of- x equals 2 x plus three find f-of-negative-one"). You used to say " y = 2 x 3 solve for y when x = −1". For functions, the two notations mean the exact same thing, but " f ( x)" gives you more flexibility and more information. The same is true of " y" and " f ( x)" (pronounced as "eff-of-eks"). Variables are more flexible, easier to read, and can give you more information. Characterising functions including worked examples on periodic, odd and even functions.In other words, they switched from boxes to variables because, while the boxes and the letters mean the exact same thing (namely, a slot waiting to be filled with a value), variables are better.These workbooks produced by HELM are good revision aids, containing key points for revision and many worked examples. The function repeats itself on intervals of length $2\pi$ which can also be clearly seen from a graph. Any function which is not periodic is called aperiodic.Įxample: The sine function is periodic with period $2\pi$ since $\sin(x 2\pi)=\sin x$ for all values of $x$. Periodic functions are used to describe oscillations and waves, and the most important periodic functions are the trigonometric functions. A function $f$ is said to be periodic with period $P$ if: \ for all values of $x$ and where $P$ is a nonzero constant. Periodic Functions DefinitionĪ periodic function is a function that repeats itself in regular intervals or periods. Note: the sum of an even and odd function is neither even nor odd, unless one of the functions is equal to zero over the given domain. The composition of an even function and an odd function is even. ![]()
0 Comments
Leave a Reply. |