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video about comparing linear and nonlinear functions

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video about comparing linear and nonlinear functions

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Does the following table represent a linear equation? So let's see what's going on here. When x is negative 7, y is 4. Then when x is negative 3, y is 3. So let's see what happened to what our change in x was. So our change in x-- and I could even write it over here, our change in x. So going from negative 7 to negative 3, we had an increase in 4 in x. And what was our change in y? And this triangle, that's just the Greek letter delta. It's shorthand for "change in." Well, our change in y when x increased by 4, our y-value went from 4 to 3. So our change in y is negative 1. Now, in order for this to be a linear equation, the ratio between our change in y and our change in x has to be constant. So our change in y over change in x for any two points in this equation or any two points in the table has to be the same constant. When x changed by 4, y changed by negative 1. Or when y changed by negative 1, x changed by 4. So we have to have a constant change in y with respect to x of negative 1/4. Let's see if this is true. So the next two points, when I go from negative 3 to 1, once again I'm increasing x by 4. And once again, I'm decreasing y by negative 1. So we have that same ratio. Now, let's look at this last point. When we go from 1 to 7 in the x-direction, we are increasing by 6. And when we go from 2 to 1, we are still decreasing by 1. So now this ratio, going from this third point to this fourth point, is negative 1/6. So it is not. So just for this last point right over here, for this last point, our change in y over change in x, or I should say, really, between these last two points right over here, our change in y over change in x-- let me clear this up. Let me make it clear. So just between these last-- in magenta. Just between these last two points over here, our change in y is negative 1, and our change in x is 6. So we have a different rate of change of y with respect to x. Because we had a different rate of change of y with respect to x, or ratio between our change in y and change in x, this is not a linear equation. No, not a linear equation.

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Linear & nonlinear functions: table (video) | Khan Academy

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Does the following table represent a linear equation? So let's see what's going on here. When x is negative 7, y is 4. Then when x is negative 3, y is 3. So let's see what happened to what our change in x was.

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website about Comparing linear and nonlinear functions-

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Linear vs. Nonlinear

You can divide up functions using all kinds of criteria:

But some distinctions are more important than others, and one of those is the difference between linear and nonlinear functions. In this lesson, you'll learn all about the two different types, how to tell them apart, and what they look like on a graph.

Graphing Linear and Nonlinear Functions

We'll start with a graph because graphing makes it easiest to see the difference. The word 'linear' means something having to do with a line.

On a Cartesian Plane, a linear function is a function where the graph is a straight line. The line can go in any direction, but it's always a straight line.

A nonlinear function has a shape that is not a straight line. Here are some examples:

But why are some functions straight lines, while other functions aren't? Look at these graphs of some linear and nonlinear functions. Can you guess what the important difference is that makes the functions on the left linear, and the functions on the right nonlinear?

What Makes a Function Linear?

Did you guess the difference between linear and nonlinear functions? The important difference is all in the exponents.

Take a look at all these functions. The linear functions don't have any exponents higher than 1. Some of them don't have variables at all, and if they do, they have just plain x, which is equal to x to the first power.

When a linear function is written in its simplest form, it looks like y = a + bx, where a and b are both constants. For example, here are some linear functions:

y = 3 + 5x

y = 2 - 6x

(Note that - 6x is the same thing as + -6x)

y = 4x

(Note that this is equivalent to y = 0 + 4x)

y = 4

(Note that this equals y = 4 + 0x)

On the other hand, non-linear functions all have at least one variable raised to the power of two or more. There's no one formula for non-linear functions because they're all different. Here are some examples:

y = 3x^3 + x^2 -7

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how to recognize linear functions vs non-linear functions - video & lesson transcript | study.com

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How to Recognize Linear Functions vs Non-Linear Functions - Video & Lesson Transcript | Study.com

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You can divide up functions using all kinds of criteria: But some distinctions are more important than others, and one of those is the difference between linear and nonlinear functions. In this lesson, you'll learn all about the two different types, how to tell them apart, and what they look like on a graph.

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