Final answer:
A positive function yields positive values for all inputs, while a negative function yields negative values. An increasing function's values get larger as the input values increase, while a decreasing function's values get smaller as the input values increase.
Step-by-step explanation:
In mathematics, a function is considered positive if it yields positive values for all its inputs. This means that when you plug in any number into the function, the result will be greater than zero. For example, the function f(x) = x + 2 is positive because no matter what value you choose for x, the output will always be greater than zero.
On the other hand, a function is negative if it yields negative values for all its inputs. This means that when you plug in any number into the function, the result will be less than zero. For example, the function g(x) = -x - 1 is negative because no matter what value you choose for x, the output will always be less than zero.
A function is said to be increasing if its values increase as the input values increase. In other words, as you move from left to right along the graph of the function, the function's values get larger. For example, the function h(x) = x^2 is increasing because as x increases, the values of h(x) also increase.
Conversely, a function is decreasing if its values decrease as the input values increase. In other words, as you move from left to right along the graph of the function, the function's values get smaller. For example, the function j(x) = -x^2 is decreasing because as x increases, the values of j(x) decrease.
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