Find out equation is a function, Mathematics

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

                           y= 5x + 1


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.

Posted Date: 4/6/2013 6:19:22 AM | Location : United States

Related Discussions:- Find out equation is a function, Assignment Help, Ask Question on Find out equation is a function, Get Answer, Expert's Help, Find out equation is a function Discussions

Write discussion on Find out equation is a function
Your posts are moderated
Related Questions
We are until now going to suppose that there will be no external forces acting on the system, along with the exception of damping obviously. Under this case the differential equati

Anne, Betty and Carol went to their local produce store to buy some fruit. Anne bought one pound of apples and two pounds of bananas and paid $2.11. Betty bought two pounds of appl


Perform each of the following algebraic expression as instruction says;- I.Multiply 5x+6m+4y by5 II.Divide 4ax+6ay-10az by 2a

A train covered a certain distance at a uniform speed.  If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time.   And if the train were

Ask question #Minimum 100 words accepted

A card is drawn from a well shuffled deck of cards (i) What are the odds in favour of getting spade? (Ans: 1:3, 3:1, 3:10, 1:25) (ii)  What are the odds against getting a spa

Curvature - Three Dimensional Space In this part we want to briefly discuss the curvature of a smooth curve (remind that for a smooth curve we require → r′ (t) is continuou