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Why can't a vertical line be used to represent rate of change?
the rate of change is related to the slope; the higher the slope, the higher the rate. If the line is vertical, that is infinite slope or infinite rate of change which is not possible
What is the rate of change for linear equations?
It is the gradient: the change in the vertical direction divided by the change in the horizontal direction.
How do you know if a function has a constant or variable rate of change?
If the graph is a non-vertical straight line, then the rate of change is constant. If the line is curved, then the rate of change (slope) varies.
How does average change help find instant rate of change in math?
This is done with a process of limits. Average rate of change is, for example, (change of y) / (change of x). If you make "change of x" smaller and smaller, in theory (with certain assumptions, a bit too technical to mention here), you get closer and closer to the instant rate of change. In the "limit", when "change of x" approaches zero, you get the true instantaneous rate of change.
How do you graph trigonometric functions?
You find the average rate of change of the function. That gives you the derivative on different points of the graph.
