Find out equation is a function, Mathematics

Assignment Help:

Example: Find out which of the following equations functions are & which are not functions.

                           y= 5x + 1

Solution

The "working" definition of function is saying is that if we take all of possible values of x & plug them in the equation & solve for y we will get accurately one value for each value of x.  At this stage it can be pretty hard to actually illustrate that an equation is a function thus we'll mostly talk our way through it. Conversely it's frequently quite easy to show that an equation isn't a function.

So, we need to illustrate that no matter what x we plug in the equation & solve for y we will only obtain a single value of y.  Note as well that the value of y will probably be different for each value of x, although it doesn't have to be.

Let's begin by plugging in some of the values of x and see what happens.

x= -4 : y= 5 ( -4) + 1 = -20 + 1 = -19

x= 0: y= 5 (0)+ 1 = 0 + 1 = 1

x= 10 : y= 5 (10) + 1 = 50 + 1= 51

Thus, for each value of x we obtained a single value of y out of the equation.  Now, it isn't enough to claim that this is a function.  To officially prove that it is a function we have to illustrates that this will work no matter that value of x we plug into the equation.

Certainly we can't plug all possible value of x in the equation. That just isn't possible physically.  For each x, on plugging in, first we multiplied the x by 5 and after that added 1 onto it.  Now, if we multiply any number by 5 we will obtain a single value from the multiplication.  Similarly, we will only get a single value if we add 1 onto a number. So, it seems plausible that depend on the operations involved with plugging x into the equation that we will just get a single value of y out of the equation.

Hence, this equation is a function.


Related Discussions:- Find out equation is a function

Example on abels theorem, Without solving, find out the Wronskian of two so...

Without solving, find out the Wronskian of two solutions to the subsequent differential equation. t 4 y'' - 2t 3 y' - t 8 y = 0 Solution : First thing that we want to d

The shortest distance among the line y-x=1 and curve x=y^2, Any point on pa...

Any point on parabola, (k 2 ,k) Perpendicular distance formula: D=(k-k 2 -1)/2 1/2 Differentiating and putting =0 1-2k=0 k=1/2 Therefore the point is (1/4, 1/2) D=3/(32 1/2

Applied mathematics, I have a journal article in applied mathematics and wa...

I have a journal article in applied mathematics and want to analyze the solutions step by step. Is there anyone specialize in this file?

Ratio, 2qt :6qt::x :48? help me solve x

2qt :6qt::x :48? help me solve x

Common graphs, Common Graphs : In this section we introduce common graph o...

Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example   Graph y = - 2/5 x + 3 .

Rita, Calculate 50%

Calculate 50%

Calculate the probability, Let D = 1 denotes the event that an adult male h...

Let D = 1 denotes the event that an adult male has a particular disease. In the population, it is known that the probability of having this disease is 20 percent, i.e., Pr (D = 1)

How to find value in polynomial?, Example  Find the values of the ...

Example  Find the values of the given expressions. Also given that a = 2, b = 3, c = 1, and x = 2. 8a + 5bc          =       8.2

Explain basic geometric concepts, Explain Basic Geometric Concepts ? P...

Explain Basic Geometric Concepts ? Points, lines, and planes are the most fundamental concepts in the study of geometry. Points A point has no length, width or heig

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd