1.3
Functions
July 17, 2025
Shivohm Karogal
3
Min Read
AI Summary
These notes explain that a function assigns each input exactly one output, forming a foundational concept in algebra. Functions can be represented in verbal, tabular, algebraic, and graphical forms, and classified as linear (with a constant rate of change) or non-linear. Linear models can be built by organizing input-output pairs, plotting them, and identifying whether the function is increasing or decreasing.
Objective
Understand what functions are and how to use them in problem-solving.
Core Concept
Functions link each input to a single output and are foundational in algebra and modeling.
Function
A function is a rule that assigns each input (X) exactly one output (Y).
Example: If f(x) = x - 2 and x = 4, then f(4) = 2.
Compare Function Properties
Verbal: Describing the function in words.
Tabular: Using a table of values.
Algebraic: Through equations (e.g., y = 3x + 5).
Graphical: By plotting points to form a straight line or curve.
Recognizing Linear vs. Non-Linear Functions
Linear Function
y = mx + c
Graph is a straight line, consistent rate of change
Non-Linear Function
Not in the form y = mx + c.
e.g., quadratic, exponential
Constructing Linear Function Models
Input X and Y values into a table.
Plot the values on a graph.
Determine if the function is:
Increasing: Both X and Y grow.
Decreasing: Y decreases as X increases.