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### Course: MAP Recommended Practice>Unit 19

Lesson 25: Linear and nonlinear functions

# Recognizing linear functions

Learn to recognize if a function is linear. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• So the non-linear function in this video is a parabola?
• In Sal's table, notice that every value of y equals 10 plus x^2
When x = 1, y = (1)² + 10 = 11
When x = 2, y = (2)² + 10 = 14
When x = 3, y = (3)² + 10 = 19
When x = 4, y = (4)² + 10 = 26
When x = 5, y = (5)² + 10 = 35
So, in each case shown in the table, y = x² + 10 and that is definitely a quadratic. A quadratic describes the points that make a parabola.

Technically, though, we don't know if this function is continuous or if it is defined by that table and only has `those 5 points`. Sal only said that the function contains those points and no one tells us that there are any other points in the function. We haven't been told if x = 0 is included or x = 1/2 or x = -3

Anyway, those points in the table do lie on a parabola--we just don't know if there are any points between those. If the problem said that the function was defined by
y = x² + 10, or if it showed the curve of a parabola with those points on it, then we would know that all the points were included. . . but then the video wouldn't be making Sal's point which is how you can know that a function is linear just by looking at the table and this one is definitely not linear.
• So would a function with the following points be a linear function?
(1,1)
(2,4)
(4,7)
(8,10)
(16,13)
(32,16)
The change in x is constant, it's always x times 2.
The change in y is constant, it's always y plus 3.
But when these points are plotted on a graph, there is no straight line between them?
How can you have a constant change in x and y but a nonlinear function?
• well, you are not having a constant change in x and y.
To go from x = 1 to x = 2, you add 1. to go from y = 1 to y = 4, you add 3. it's okay for now. But to go from x = 2 to x = 4, you add 2, so you should add 3*2 =6 to the previous y (i.e.,4) to get 10, but you added only 3 to get 7.
• how do I know if a function is linear or not when it is explained like this: f(x)=x-11; (4) ?
• When the variable (x) has a exponent of 1 (or you do not see one because 1 is understood) it represents a line which is length. Length is usually in units of cm, m, etc...
(1 vote)
• Would something like y=3 be linear or nonlinear?
• Any equation in the format y=n(n stands for a number) or x=n will be linear.
• So can negative number also be linear or is that just for positive numbers
• Linear equations can have negative values in them! For example:
x y
-2 -5
-1 -3
0 -1
1 1
This set of values is linear, because every time x increases by 1, y goes up 2 so there is the same interval between each y value. This works even though there are negative numbers!
• I still don't get what a linear functions is?
• A linear function refers to when the dependent variable (usually expressed by 'y') changes by a constant amount as the independent variable (usually 'x') also changes by a constant amount. For example, the number of times the second hand on a clock ticks over time, is a linear function. Every minute (the constant change in x) the second hand ticks 60 times (the constant change in y). This is a linear function because for every 1 minute, the clock ticks the same number of times. If we express this situation on a graph, we would observe a straight diagonal ray, starting at (0,0) and increasing towards the upper right. As x (minutes) increases by 1, y (number of ticks) would increase by 60.
• I would ask for help but are people still on here to ask?
• Yes, I would love to help I am not good at math but I can try and help you a little! What do you need help with? I will give you the most help I can!
• i dont understand like the x and y dont dont agree with there constants
• At you talk about seeing if it's Linear by dividing the change in Y by the in change X. I did not understand that?
• It means he is dividing the amount between the Y numbers by the amount between the X numbers.
Example:
X Y 14-11= 3 2-1=1
1 11
2 14 3/1= 3