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

Word problem, tom has 150 feet of fencing to enclose a rectangular garden. ...

tom has 150 feet of fencing to enclose a rectangular garden. if the length is to be 5 feet less than three the width, find the area of the garden

About matrix?, Explain sparse matrix and Dense matrix?

Explain sparse matrix and Dense matrix?

Derive a linear system - gauss jordan elimination, Suppose that, on a certa...

Suppose that, on a certain day, 495 passengers want to fly from Honolulu (HNL) to New York (JFK); 605 passengers want to fly from HNL to Los Angeles (LAX); and 1100 passengers want

Share and dividend, give me a proper project on share and dividend of minim...

give me a proper project on share and dividend of minimum 25 pages

Geometry, In the diagram points V,W,X,Y and Z are collinear, VZ=52, XZ= 20 ...

In the diagram points V,W,X,Y and Z are collinear, VZ=52, XZ= 20 AND WX=XY=YZ. Find the indicated length of WX, VW, WY, VX, WZ, and VY

Periodicity, how to find periods in trigon ometry

how to find periods in trigon ometry

Sequencing model, theory about solving sequencing problem using graphical m...

theory about solving sequencing problem using graphical method

Solid Mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

Eometry constructions, construct an isosceles triangle ABC when:base BC is ...

construct an isosceles triangle ABC when:base BC is 6.2 and altitude a.a

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