|
Question 178732: What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function. Create an equation of a nonlinear function and provide two inputs.
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! functions map inputs to UNIQUE outputs. A polynomial function of the first degree, such as y = 2x + 1, is called a linear function
All linear equations are functions with the exception of one type--
:
Usually on uses the vertical line rule to see if an equation is a function or not. If a vertical line intersects a graphed equation at more than one point, the equation is NOT a function.
:
As stated, there is a linear equation that is not a function. Using the vertical line rule we can conclude that a vertical itself is not a function. Maybe it would be easier to look at this from another description of function. There is one and only one y value for each value of x in a function. For x=a, there is infinite values of y. Thus a vertical line is not a function.
nonlinear function f(x) = x^2-1
:
f(1)=0...(1,0)
f(2)=3...(2,3)
|
|
|
| |
