Glossary
Assumptions (in models)
Conditions or principles presumed to be true and consistent within a mathematical model, simplifying reality to make predictions.
Example:
A model predicting population growth might make the assumption of a constant birth rate.
Degree of a Polynomial
The highest exponent of the variable in a polynomial function, which indicates the maximum number of real roots and influences the function's end behavior.
Example:
In the function y = 3x⁴ - 2x + 7, the degree of the polynomial is 4.
Domain Restrictions
Limitations on the possible input values (x-values) of a function, determined by mathematical rules or the real-world context of the problem.
Example:
In a function modeling the number of hours worked, the domain restriction would be that hours cannot be negative.
Function Model
A mathematical representation of a real-world situation, simplifying reality to understand and predict outcomes.
Example:
Using a function model like y = 2x + 5 to predict the cost of a taxi ride based on distance.
Linear Function
A function characterized by a constant rate of change, represented by the equation y = mx + b.
Example:
The growth of a plant at a steady rate of 2 cm per day can be modeled by a linear function.
Piecewise Function
A function defined by multiple sub-functions, each applicable over a specific interval of the independent variable's domain.
Example:
A cell phone plan that charges different rates for data usage above a certain limit is an example of a piecewise function.
Polynomial Function
A function composed of multiple terms, each with a constant coefficient and a non-negative integer exponent, used to model complex behaviors with multiple turning points.
Example:
Modeling the fluctuating temperature of a city over a year might require a higher-degree polynomial function.
Quadratic Function
A function used for situations with a changing rate of change or a symmetrical parabolic shape, typically written as y = ax² + bx + c.
Example:
The path of a basketball shot through the air can be accurately modeled by a quadratic function.
Range Restrictions
Limitations on the possible output values (y-values) of a function, determined by mathematical rules or the real-world context of the problem.
Example:
If a function models the height of a thrown ball, a range restriction would be that the height cannot be below zero (ground level).
Slope (m)
In a linear function, the slope (m) represents the constant rate at which the dependent variable changes with respect to the independent variable.
Example:
If a car travels 60 miles per hour, its speed is the slope of the distance-time graph.
Y-intercept (b)
In a linear function, the y-intercept (b) is the value of the dependent variable when the independent variable is zero, representing the starting point.
Example:
The initial fee for a rental car before driving any miles is the y-intercept of the cost function.