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What does a graph tell you?

Updated: 4/28/2022
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14y ago

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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.

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14y ago
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Q: What does a graph tell you?
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