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If the function is continuous in the interval [a,b] where f(a)*f(b) < 0 (f(x) changes sign ) , then there must be a point c in the interval a<c<b such that f(c) = 0 .
In other words , continuous function f in the interval [a,b] receives all all values between f(a) and f(b)
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What kind of verticle-line test determines which graph represents a function?
A sliding test. The vertical line can meet the graph at at most one point.
What is infinity divided by pi?
Impossible to answer ! Infinity is a never ending quantity - and Pi is a never ending decimal !
What is the relationship between the domains and ranges of a function and its inverse?
The domain of a function, f(x), is a set of real numbers (call them values of x) which corresponds to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range ( y- value). So the range is the set of real numbers that are values of the function. An inverse of a function f(x) is denoted by f-1(x) where -1 is NOT an exponent. The notation f-1 does not mean 1/f (so it looks like a neg 1 exponent but it is not. Math people know to read this as the inverse function). Any function that passes the horizontal line test (which intersects the graph of the function only once) has an inverse, also it is a one-to-one function. Any one-to-one function has a graph that passes the horizontal line test. A one-to one function is a function in which not two different pairs have the same second component. For this kind of functions (one-to-one functions), the domain becomes the range for the inverse and vv. It means that if a point (x, y) is on the graph of f, then the point (y, x) is on the graph of f-1. Ex: y or f(x) = x2 (the domain is the set of all real numbers. you can square positives, negatives, fractions etc. the range is only all reals greater than or equal to zero). The graph of f(x) = x2 does not pass the horizontal test, because it intersects the graph at two points, let's say (-3, 9) and (3, 9). Inverse functions have ordered pairs with the coordinates reversed. If we interchange x- and y-coordinates then we obtain (9, -3) and (9, 3) but these ordered pairs do not define a function. Thus this function does not have an inverse. But if we restrict the domain, for example the set of all positive numbers including zero, then we allow it to have one, and this inverse function f-1 is a reflection of the graph of f about the line y = x, where f(x) = x2 and its domain is {x| x ≥ 0}. The inverse of the above function is the square root of x. which I will abbreviate as sq rt the inverse function becomes f-1(x) = √x (in other words, f you limit yourself to real numbers, you cannot use any negatives in place of x for this inverse function. So the domain of the inverse is all reals > or = 0. If the inverse is to be a function you cannot have any answers which are negative. the relation would not pass the vertical line test. so the range is also only reals > or = zero).
What kind of number is -8?
A negative one.
What kind of clothes does Calvin Klein design?
topay
What kind of distribution is exponential distribution?
Exponential distribution is a function of probability theory and statistics. This kind of distribution deals with continuous probability distributions and is part of the continuous analogue of the geometric distribution in math.
What kind of electricity is caused by a continuous flow of electrons?
what kind of electricity is caused by a continuous flow of electrons
Can it be possible limit of logarithmic functions equal to logarithmic function of limit?
Yes it is possible.If limit(f) > 0 then limit(loga(f)) = loga(limit(f)).All logarithmic functions loga(x) are continuous as long as x > 0. Where-ever a function is continuous, you can make that kind of swap.
What kind of variable is temperature change?
Temperature change is a continuous and interval variable, meaning it can take any real value within a certain range and the differences between values are consistent.
Why do pine trees never change year round?
Because they are a kind of Evergreen.
What kind of distribution does a baby's weight represent?
Continuous
Is going is what kind of tense?
Present continuous tense.
The amount of posts in your class at a given time represents what kind of distribution?
continuous
What kind of electricity is caused by a continuous flow of electricity?
Current electricity is the kind of electricity that is caused by a continuous flow of electricity. In order for this to happen there must be a voltage present across a conductor, for example in overhead power lines.
Why are the y-values of an exponential growth function either always greater than or less than the asymptote of the function?
The exponential function is always increasing or decreasing, so its derivative has a constant sign. However the function is solution of an equation of the kind y' = ay for some constant a. Therefore the function itself never changes sign and is MORE?
What kind of dress never be worn?
An address is the kind of dress that can never be worn.
What is the variation in human skin color an example of?
This is a typical kind of continuous variation which is controlled by polygenes.
