What does a graph tell you?

Answer 1

A graph of an equation (or function) helps to clarify the behavior of that equation. In this case, the behavior of the graph is just that: it describes how something acts-- for example:

• Whether it is a straight line or a bending curve
• How many times it changes direction and where
• Whether the y-value becomes greater or smaller (moves up or down), or stays constant, as it moves from left to right
• If it is discontinuous (skips around without warning, turns sharply, flies up into infinity for a while, or simply vanishes for a short time)
• What the equation must look like, such as a line for a linear equation (y = mx + b) or a parabola for a quadratic equation (y = ax2 + bx + c)
• When the equation crosses the x-axis, something that is very useful to know in Algebra and later mathematics
• How fast the equation is increasing or decreasing
• In Calculus, a graph can be used to find the derivative of a function, which is a new function that describes the slope of a function at each point

In general, a graph is a very useful tool to understand how an equation works, and can make encounters with new and unfamiliar forms of equations easier to understand.