If the problem is f(x)= -6x+3 what can help me detirmine if the function is linear or nonlinear?

Expert Answers
steveschoen eNotes educator| Certified Educator

There can be several ways to do this.  First, what I would do is, for all practical purposes, f(x) just means y.  So, we would have:

y = -6x+3

Then, if you have learned that all linear functions can be written in the form:

y = mx+b

and see that "y = -6x + 3" is written in that form, also.  Then, y = -6x+3 must be linear.

Or, if you tried to graph y = -6x+3, as in making a table:

x     1     2     3     4     5

y    -3    -9   -15  -21  -27

When you plot an infinite number of points, the graph would show a straight line, thus, a linear function.  For practical purposes, all you need are 2 points to draw a straight line, though.  Some teachers require 3 points, the 3rd point being a check on your math for the first two.

msburch eNotes educator| Certified Educator

` ` The quickest way that you can determine if something is a linear function is by looking at the variables given. 

If you do not have exponents greater than 1 for either variable, you can determine that it will be a linear function. 

f(x)= -6x+3

In this case, f(x) can be replaced merely with y. 

You have y = -6x + 3. Because both of the variable terms are in the 1st degree, this will be a linear function. 

Examples of non-linear functions for reference:
 `y = x^2`

`y = xy`

`y = 1/x`

`y^2 = 3x `

`y= sqrt(x)`

ishpiro eNotes educator| Certified Educator

Another way to determine if the function is linear is to look at the powers of x and y.

If both x and y are in the first power, then the function is linear, like the given example y= -6x + 3.

If there is y in the equation but no x (for example, y = 5), the function is still linear.

If either y or x is in the higher power of (such as `x^2` ), or there are other operations on x (such as `1/x ` or `sqrt(x)` ), the function will not be linear.

embizze eNotes educator| Certified Educator

Remember that for a function to be linear, each term must have degree 1 or 0.

Consider the function xy=4; both x and y appear to the first power, but this is a hyperbola, certainly not linear. Note that xy has degree 2.

ishpiro eNotes educator| Certified Educator

Yes, this answer was given with assumption that the function was written in the form

y = f(x)

as opposed to as any equation for relating x and y.