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Today, we are going to talk about functions and how they can be applied in real life situation. But first, what are functions? Do you have any idea about what functions are? And now, I am going to start giving you a definition. Are you ready? Let's go!
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
It is also a bunch of ordered pairs of things (in your case, the things will be numbers, but they can be otherwise), with the property that the first members of the pairs are all different from one another.
IN OTHER WORDS, a function is a mathematical relationship between two variables, where every input variable has one output variable.
DEPENDENT AND INDEPENDENT VARIABLES
In functions, the x-variable is known as the input or independent variable, because its value can be choosen freely. The calculated y-variable is known as the output or dependent variable, because its value depends on the chosen input value.
SET BUILDER NOTATION
A shorthand used to write sets, often sets with an infinite number of elements.
TYPES OF FUNCTIONS
Constant function is a linear function of the form y=b, where b is a constant. It is also written as f(x)=b. The graph is a horizontal line.
Identity function: It can be written in the form f(x)=x. It's graph is a straight line passing through the origin.
Linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. It is written in the form f(x)=mx+b. It's graph is a straight.
Radical function contain functions involving roots. Most examples deal with square roots.
Piecewise function is a function that is defined as a sequence of intervals.
Quadratic function is one of the form f(x)=ax2+bx+c, where a, b and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.
DOMAIN OF A FUNCTION
The domain of a function is the set of all independents x-values for which there is one dependent y-value according to that function.
RANGE OF A FUNCTION
The range of a function is the set of all dependent y-values which can be obtained using an independent x-value.
EXAMPLE OF DOMAIN AND RANGE
NOW WE ARE READY
Functions are mathematical building blocks for designing machines, predicting natural disasters, curing diseases, understanding world economies and for keeping aeroplanes in the air. Functions can take input from many variables, but always give the same output, unique to that function.
Money as a function of time. You never have more than one amount of money at any time because you can always add everything to give one total amount. By understanding how your money changes over time, you can plan to spend your money sensibly.
Temperature as a function of various factors. Temperature is a very complicated function because it has so many inputs, including: the time of day, the season, the amount of clouds in the sky, the strength of the wind, where you are and many more. But the important thing is that there is only one temperature output when you measure ir in a specific place.
Location as a function of time. You can never be in two places at the same time. If you were to plot the graphs of where two people are as a function of time, the place where the lines cross means that the two people meet each other at that time. This idea is used in logistics, an area of mathematics that tries to plan where people and items are for businesses.
Now we are going to learn how quadratic functions can be applied in real life situations.
The throw ends when the shot hits the ground. The height y at that point is 0, so set the equal to zero.
This equation is difficult to factor or to complete the square, so well solve by applying the quadratic formula.
Simplify or find both roots. x=46.4 or -4,9.
Do the roots make sense? The parabola described by the quadratic function has two x-intercepts, but the shot only traveled along part of that curve.
One solution, -4,9, cannot be the distance traveled because it is a negative number.
The other solution, 46,4 feet, must give the distance of the throw.
Now that we've studied different types of function and how a quadratic function can be applied in real life, we now say that everything can related in real life and that these can be solved through these mathematical equations learned in school.
I hope you had a nice time watching this video, thank you!
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