Lesson 4: Graphing Functions

How do we decide good value of x for a function graph?
How many ordered pairs do we need to create a good graph of a function?

F.IF.1
A. Understand the concept of a function and use function notation
1. HSF-IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of
the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the
equation y = f(x).

2. HSF-IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

B. Interpret functions that arise in applications in terms of the context
5. HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.?

Lesson Description: This lesson focuses on the visual representation of functions f(x) on a coordinate plane. While the mechanics of plotting are similar to previous sections, the emphasis shifts to the unique properties of functions. Students will: Construct Function Tables: Using x as the input and f(x) as the output (replacing the traditional y-column).Graph Linear Functions: Plotting the set of all ordered pairs (x, f(x)) that satisfy a linear rule .Identify Function "Behaviors": Recognizing how changes in the function’s formula (such as changing the constant or the coefficient) shift or tilt the graph. Vertical Line Test (Advanced): Re-applying the VLT to confirm that the graphs they have created represent valid functions where every input has a unique output.
Purpose
The purpose of Section 8.4 is to achieve visual-symbolic synthesis. By graphing functions, students see that f(x) = mx + b is not just a string of characters, but a geometric path with a specific trajectory. This section reinforces the idea that the "output" of a function is the vertical height of its graph. This is a crucial mental model for students moving into MAT 137 and higher, where they will eventually graph more complex shapes like parabolas and exponential curves.
Depth of Knowledge (DOK) Level
DOK Level 2
Level 2 (Skill/Concept): Students must translate a symbolic function into a visual graph. This requires coordinating multiple steps: choosing appropriate inputs, calculating outputs using function notation, and correctly scaling and plotting the result. It also involves identifying the relationship between the function's symbolic form and its graphical landmarks (like intercepts).

Function notation is sometimes difficult for student to comprehend. Stress that f(x) does not mean "f times x."

Class and online work

use "you try" pg 186 and practice problems  to assess students' understanding of the lesson concepts