1. 8.6.4 Comparing Linear and Nonlinear Functions

2. Linear vs. Nonlinear Functions
Linear Function = Must be a line, must cross the y-axis (can’t be a vertical line), the line has a consistent rate of change, doesn’t increase or decrease, the change is always the same
Nonlinear Function = Not a line, or doesn’t cross the y-axis, or is a vertical line, or the rate of change isn’t consistent
Cool Math Fact! The slope of a vertical line is undefined because you can’t divide anything by zero!
Find the slope: (3, 5) and (3, 7)
Change in y = 7-5 = 2
Change in x = 3-3 = 0

3. Linear or Nonlinear? Identifying Functions from TablesX 3 6 9 12 Y 40 32 24 16
As x increases by 3, y decreases by 8. The rate of change is constant. The function is linear.

4. Linear or Nonlinear? Identifying Functions from TablesX 1 3 5 7 Y 2 11 33 88
As x increases by 2, y increases by different amounts. The rate of change is not consistent. So the function is not linear.

5. Linear or Nonlinear? Identifying Functions from Graphs

6. Linear or Nonlinear? Identifying Functions from Graphs
It’s not a line, so it’s nonlinear.

7. Linear or Nonlinear? Identifying Functions from Graphs

8. Linear or Nonlinear? Identifying Functions from Graphs
It’s a line and it’s not vertical, so it’s linear.

9. Linear or Nonlinear? X 7 14 21 Y 25 20 15 10 X 2 4 6 8 Y -4

10. Identifying a Nonlinear Function
The A. function has no slope, but it does have a y-intercept of 4.7 meaning it’s a straight line through that point on the y-axis. So function A. is a linear function.
The B. function has a slope of Π, or 3.14, and without a y-intercept listed, the line must pass through the origin (0,0). So function B. is a linear function.
The C. function doesn’t have a y-intercept listed and it doesn’t have a slope either as the slope in a linear function is multiplied by x, not divided by x. So function C. is a nonlinear function.
The D. function can be rewritten as y = 4x – 4, a perfect linear equation. So function D. is a linear function.
Which equation represents a nonlinear function?
y = 4.7
B. y = Πx
C. y = 4 x
D. y = 4(x – 1)

11. Identifying a Nonlinear Function
Does the equation represent a linear or nonlinear function?
y = x + 5
B. y = 4x 3
C. y = 1 - x²

12. Suggested Practice
Page 270 (#1, 2, 5, 6, 8, 10, 11, 12, 13, 14, 17, 18)