If f(x) is increasing on the interval from x = 2 to x = 10, and if g(x) is decreasing on the interval from x = 2 to x = 10, then the function (f + g)(x) will be constant on the interval from x = 2 to x = 10.
true or false
false, probably. It depends on the difference in the amount of increase/decrease each has
What is the end behavior of this function 6x^8+2x^3+8-7
To determine if the function (f + g)(x) is constant on the interval from x = 2 to x = 10, we need to consider the properties of increasing and decreasing functions.
Since f(x) is increasing on the interval from x = 2 to x = 10, this means that as x increases within this interval, the corresponding values of f(x) also increase. On the other hand, g(x) is decreasing on the same interval, which means that as x increases, the corresponding values of g(x) decrease.
When we add these two functions, (f + g)(x), we are essentially summing the corresponding values of f(x) and g(x) at each point on the interval.
Since f(x) is increasing and g(x) is decreasing on the same interval, it is possible for the increase in f(x) to offset the decrease in g(x), resulting in a constant value when the two functions are added.
Therefore, it is true that the function (f + g)(x) will be constant on the interval from x = 2 to x = 10.