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

Substitution rule for definite integrals, Substitution Rule for Definite In...

Substitution Rule for Definite Integrals Now we need to go back and revisit the substitution rule as it also applies to definite integrals.  At some level there actually isn't

0^0, what is the value of zero to the power raised to zero?

what is the value of zero to the power raised to zero?

Draw a common graph y = sin ( x ), Graph y = sin ( x ) Solution : As a...

Graph y = sin ( x ) Solution : As along the first problem in this section there actually isn't a lot to do other than graph it.  Following is the graph. From this grap

How many years will it take him to pay off the loan, Joe took out a car loa...

Joe took out a car loan for $12,000. He paid $4,800 in interest at a rate of 8% per year. How many years will it take him to pay off the loan? Using the easy interest formula I

Point-slope form, The next special form of the line which we have to look a...

The next special form of the line which we have to look at is the point-slope form of the line. This form is extremely useful for writing the equation of any line.  If we know that

Can u please tell me how to solve, a triangle with side lengths in the rati...

a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3.what is the area of the triangle.

Example for comparison test for improper integrals, Example for Comparison ...

Example for Comparison Test for Improper Integrals Example:  Find out if the following integral is convergent or divergent. ∫ ∞ 2 (cos 2 x) / x 2 (dx) Solution

The unitary method, i want detail information in advance with question and ...

i want detail information in advance with question and answers.

Proof of constant times a function, Proof of Constant Times a Function: ...

Proof of Constant Times a Function: (cf(x))′ = cf ′(x) It is very easy property to prove using the definition given you a recall, we can factor a constant out of a limit. No

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