LF - Linear vs. Nonlinear Lesson

Linear vs. Nonlinear

Now, how do we know if a function is linear or non-linear? A linear function is defined as a first-degree polynomial. This simply means that the exponent of the x is 1. A linear function can also be written in the slope-intercept form we've discussed, y = mx + b where m represents the slope and b represents the y-intercept.

Here are some examples of equations that are linear functions:

  1. y = 2x + 1
  2. y = -1/2x - 4
  3. y = x

Here is an example of a linear function graph (notice it is a straight line):

 image of negative straight line on graph

Here is an example of a linear function written in a table:

x

0

2

4

6

y

1

2

3

4

What would a non-linear function look like?   Let's look at a few examples of functions that are not linear functions.

  1. y = x2 + x + 3
  2. y = |x| - 8
  3. image of upward facing parabola on graph

(Notice this is not a straight line, so it is not a linear function.)

You try! Determine if each of the following are linear or non-linear.

Assignment

Now that you have spent some time learning about linear vs. non-linear functions, you are ready to complete your Linear vs. Non-Linear Homework. Click here to download the Linear vs. Non-Linear Homework Links to an external site..

Once you have completed the Linear vs. Non-Linear Homework, check your even answers and make sure you ask your teacher if you have any questions. Links to an external site. When you feel confident in your work, you'll need to take the Linear vs. Non-Linear Homework Quiz. Make sure you have your Homework completed and with you when you log in to take it. This is a timed quiz and you'll only have time to enter the answers from your HW. You will not have time to work them out during the quiz.

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