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Consider the function y = an
If a < -1 it oscillates between negative and positive values, with the oscillations increasing.
If a = -1, it oscillates between -1 and 1.
If -1 < a < 0 it oscillates between negative and positive values, with the oscillations deceasing.
if 0 < a < 1, it is decreasing.
If a = 1, it is 1 for all n
If a > 1, it is increasing.
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How can you tell from a linear equation which direction it goes without graphing the equation?
You must find the slope, if it is positive, then the line is always increasing. If it is negative, then the line is always decreasing.
How do you tell if its exponential growth or decay?
Exponential growth has a growth/decay factor (or percentage decimal) greater than 1. Decay has a decay factor less than 1.
What does the horizontal line tell you about a function?
If the function is a one-to-one function, therefore it has an inverse.
How can you tell by looking at a graph if the represntation is a function?
if a certain abscissa corresponds to more than one ordinate, then it is not a function.
How do you tell if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
