What You Will Practice
In college math, science, and engineering, one quantity often depends on another. A function is a rule that connects an input to an output. This chapter prepares students for function thinking, graphs, rates of change, and calculus.
Mini Lesson
1. What Is a Function?
A function is a rule that gives exactly one output for each input.
Example: If a tool costs $15 per hour to rent, then cost depends on time.
2. Function Notation
Function notation tells you to evaluate the rule at a specific input.
Example: f(2) = 3(2) + 2 = 8
3. Linear Functions and Slope
A linear function changes at a constant rate. That constant rate is the slope.
Example: A tank filling at 5 liters per minute can be modeled by V(t) = 5t.
4. Quadratic Functions
Quadratic functions do not change at a constant rate. They often appear in motion, acceleration, and curved paths.
Example: h(1)=1, h(2)=4, h(3)=9. The outputs grow faster as x increases.
5. Reading Functions from Tables
A table represents a function if each input has exactly one output.
Example: Time 0, 1, 2, 3 seconds and positions 0, 3, 6, 9 meters form a function.
Interactive Functions Practice
Choose a topic and practice with instant feedback. For function equations, type answers like
C(t)=15t, d(t)=60t, or y=5x+2.
8, function, notafunction, C(t)=15t, y=3x+2.
Mastery Check
Before moving to Book 2 Chapter 3, students should be able to do the following.
Function Meaning
I can explain a function as an input-output rule.
Function Notation
I can evaluate f(x) when given an input value.
Linear Functions
I can identify the constant rate of change in a linear relationship.
Quadratics
I can evaluate a quadratic function and recognize nonlinear growth.
Tables
I can tell whether a table represents a function.