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SteveIf the y-vaue (output) of the function increases as the x-value (input) increases, the function is increasing. If the y-value (output) of the function decreases as the x-value (input) increases, the function is decreasing.
Example: y = x is always increasing. y = -x is always decreasing.
It is the increase or decrease in some measure that is put into the context of the starting value.
Generally speaking, the change from x to y is y - x.
If y is greater than x then y - x is positive and so it is an increase, while if y is less than x then y - x is negative and so it is a decrease.
The percentage increase (or decrease) is 100 times the change divided by the initial value. That is, 100*(y - x)/ x which is equal to 100*(y/x - 1)
Normally, x should be positive. Otherwise you have the situation where a change from +50 to -25 = -150%
and from -50 to +25 = -150%
The same percentage changes, but very different stories behind them!
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What are the intervals over which the function is increasing or decreasing?
It depends on the function.
Is a constant function increasing or decreasing function or both or not?
Neither, by definition.
What if the rate of change is a measure of how fast the function is increasing or decreasing what does the slope of a linear?
The slope of a linear function is also a measure of how fast the function is increasing or decreasing. The only difference is that the slope of a straight line remains the same throughout the domain of the line.
Is the function that cuts through the points 2 3 and -1 6 increasing or decreasing?
Points: (2, 3) and (-1, 6) Slope: -1 therefore it is decreasing
How can you tell if an exponential function will be decreasing of increasing?
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.
