Glossary
Average rate of change
The ratio of the change in the output (y-values) to the change in the input (x-values) over a specific interval. It represents the slope of the secant line between two points on a function's graph.
Example:
If a runner covers 10 miles in 2 hours, their average rate of change (speed) is 5 miles per hour.
Concave Down
A characteristic of a function's graph where it opens downwards, resembling a frown. In this region, the average rate of change is decreasing.
Example:
The initial path of a ball thrown upwards, before it reaches its peak, is concave down as its upward speed decreases.
Concave Up
A characteristic of a function's graph where it opens upwards, resembling a smile. In this region, the average rate of change is increasing.
Example:
The graph of a ball thrown upwards, after it reaches its peak and starts falling, is concave up as its downward speed increases.
Linear function
A function whose graph is a straight line, characterized by a constant rate of change (slope).
Example:
If your savings account grows by $50 every month, the total amount of money over time is a linear function.
Quadratic function
A function defined by a polynomial of degree two, whose graph is a parabola and has a changing rate of change.
Example:
The path of a basketball shot through the air can be modeled by a quadratic function.
Secant line
A straight line that connects two distinct points on the graph of a function. Its slope represents the average rate of change between those two points.
Example:
Drawing a line from the start of a roller coaster's first drop to the bottom of the drop creates a secant line representing the average steepness.