While studying mathematics it is hard to visualize how what we learn in class can be applied in real life. However, as every math teacher has said once in their lives, mathematics is everywhere.
A function can be found is an action as simple as putting gas in our car. Our independent variable x is the number of litres we put in, our dependent variable f(x)=y represent the amount of money we have to pay. Lets say each litre costs $1.25. The function of the price in term of the litres put into the car is: f(x)=1.25 x
The Fibonacci sequence {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …} is a list of infinite numbers where the two first items are 1, and the rest are the sum of the two items that came before. The value of each of the elements of this sequence keeps increasing indefinitely, therefore the Fibonacci sequence is divergent and it is not bounded by any number. This curious sequence can be found in the way sunflowers’ seeds or artichoke are arranged.
Figure 1. SunFlower: the Fibonacci sequence, Golden Section. Retreived from https://www.flickr.com/photos/lucapost/694780262
Finally, a real life example of a series can be found in harmonic series. As its name insinuates harmonic series exist in music. This series has the form 1+ 1/2 + 1/3 + 1/4 + 1/5+ … + 1/n
a) Does the graph of your function have a horizontal asymptote? No, it does not. It is a linear function which does not have any asymptote.
b) Does your sequence converge? No, it does not. The value of each element is increasing as n becomes larger.
c) Does your series converge? No, it does not. Harmonic series diverge.
Reference:
SunFlower: the Fibonacci sequence, Golden Section [photograph]. (2007). Retreived from https://www.flickr.com/photos/lucapost/694780262