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How do you find the domain and range of the function f of x equals half of the absolute value of x minus 2?
The domain could be the real numbers, in which case, the range would be the non-negative real numbers.
How do you determine what the domain and range of a function are?
The domain of a function pertains to all the x values The range of a function pertains to all the y values So domain and range do not get confused, this can be easily remembered by the order of the how the first letter of the word appears in the English alphabet. d, domain, goes before r, range x goes before y domain = x values range = y values ill try to add to the previous writer. previously, he wrote what the domain and range are for easier functions, but not how to determine them. more generally, what the domain is, is what you can put into a function, which in simpler cases, is jus x. to find what you can put in, it helps to find what you cant put in for x, meaning, where is the graph of the function discontinuous. for example, if we look at the function f(x)=1/(1-x) if we put 1 in for x, then the denominator goes to zero and the function is discontinuous at that x value, therefore 1 will not be included in the domain, but everything else will be included since there are no other disconinuities. the domain will end up looking like this- (-infinity,1), (1,infinity). now for the range, all you have to do is find what you can get out of the function from what you can put in, which can usually be done by putting the values you see for the domain in. putting negative infinity in for x in f(x)=1/(1-x) you get zero and putting one in you get infinty. putting it together you get (-infinity,0), (0,infinity) for your range. p.s. as i stated before, more generally, your domain is more so what you put into your function, so it is not always x, for example, in the case of a function of 2 variables such as f(x,y), what you can put in for both x and y will make up your domain, not just x, and y will most certainly not be your range, rather it will be the values of f(x,y).
How do you find the domain and range of f of x equals x squared minus 3x minus 10?
The domain is what you choose it to be. You could, for example, choose the domain to be [3, 6.5] If the domain is the real numbers, the range is [-12.25, ∞).
What is the domain of the function f x x 2 plus 4?
The domain of the function f (x) = square root of (x - 2) plus 4 is Domain [2, ∞)
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).
