Analyzing Graphs of Functions

A function is a relation that assigns exactly one output for each input. It can be represented as a graph, equation, or table.

The slope represents the rate of change of the function; it indicates how steep the line is and the direction it moves.

A constant rate of change means that the function increases or decreases by the same amount over equal intervals.

A head start is indicated by a point on the graph that is above the starting point on the y-axis before the time (x-axis) begins.

A stationary graph means that the output value does not change over time; the graph is flat.

Acceleration refers to the change in the speed of an object; in a graph, it is shown by a curve that gets steeper.

The highest point on a graph is found at the vertex of a curve or the peak of a line, indicating the maximum value.

A graph with constant speed is represented by a straight line with a consistent slope.

Speed is the distance traveled per unit of time, while velocity includes direction and is a vector quantity.

An object is moving away from the starting position if the graph shows an increasing value on the y-axis as time progresses.