Patterns, Functions, & Algebra – Linear VS Nonlinear (Notes)
Name
Date
I can …
Essential Question:
Key Concepts
Functions can either be classified as:
What are the differences between Linear and
Nonlinear:
What are the differences of equations for Linear
and Nonlinear?
What do those graphs look like?
Define –
Roots/Zeros of a Graph
Notes
Example 1 - Does the table represent a linear or
nonlinear function? Explain.
Example 2 - Does the equation represent a
linear or nonlinear function? Explain.
Example 3 - Does the graph represent a linear or
nonlinear function? Explain.
Example 4 – Determining Roots of a Graph
The graph of f(x) is shown below. What are the
zeros?
Reflection, Summary, & Analysis
Patterns, Functions, & Algebra – Linear VS Nonlinear (Exercise)
Name
Date
For questions 1 - 4, determine if the table represents a linear or nonlinear function. Explain.
1.
2.
3.
4.
For questions 5 -13, determine if the equation represents a linear or nonlinear function. Explain.
5. 𝒚 = 𝟓
8. 𝒙𝒚 = −𝟏𝟑
11. 𝒙 = 𝟒𝒚𝟐
6. 𝟐𝒙 + 𝟑𝒚 = 𝟏𝟎
7. 𝒚 = 𝟕𝒙𝟐
9. 𝒚 = 𝟑𝒙 + 𝒙𝟑
10. 𝒚 = 𝒙 + 𝟐
12. 𝒚 = √𝒙
13. 𝒚 = − 𝟒 𝒙 − 𝟐
𝟏
𝟐
𝟑
The table shows the height h (in feet) of a falling object at t seconds.



Graph the data in the table.
Decide whether the graph is linear or nonlinear.
Compare the two falling objects. Which one has an increasing speed?
Functions can either be classified as ________________ or ___________________.
Functions
Differences
Linear
1. Straight Line
Nonlinear
1. Not straight/ curve
2. The output has a constant
difference
2. The output does not have a constant rate
3. Constant rate = Slope
3. Does not have the same slope
4. Can be written in slope
intercept form
4. Cannot be written in slope intercept form
5. Has a degree of 1
5. Has a degree of more than 1. Has an exponent that
is not 1.
Linear
Quadratic
Equations
Graphs
Roots/Zeros – The x-intercepts of a graph. The x-values where the graph crosses the x-axis.
Situation 1 – Does the table represent a linear or nonlinear function? Explain.
Cubic
Situation 2 – Does the equation represent a linear or nonlinear function? Explain.
Situation 3 – Does the graph represent a linear or nonlinear function? Explain.
Situation 4 – Determine the roots.
The graph of f(x) is shown below. What are the zeros?