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Does the rate of change have to be negative?
no... the sign indicates whether the rate of change is increasing or decreasing. It is only negative if the rate is decreasing over time.
What is X2-4 divided by x2 plus 3x plus 2 continuous or discontinuous?
The numerator function x2 - 4 and the denominator function x2 + 3x + 2 are both continuous functions of x for the entire x-axis. However, the quotient of these two functions is not continuous when the denominator function has the value of 0, because division by zero is not defined. The denominator function is 0 when x = -1 or -2. Therefore, the quotient function is not fully continuous over any intervals that include -1 or -2, but it is "piecewise continuous" over other intervals of the x-axis.
How do you show log x is convex?
Log x is defined only for x > 0. The first derivative of log x is 1/x, which, for x > 0 is also > 0 The second derivative of log x = -1/x2 is always negative over the valid domain for x. Together, these derivatives show that log x is a strictly monotonic increasing function of x and that its rate of increase is always decreasing. Consequently log x is convex.
Over the set of real numbers what is the domain of the composite function GF x?
The domain of your function is the set of real numbers.
What is the reflection through an x axis?
All y-values in the function are multiplied by -1. This function is 'flipped' over the x-axis.
