How do you find the domain and range of # 2(x-3)#?

Question

Abigail Allen · Accepted Answer

Domain: #(-∞,∞)# Range: #(-∞,∞)# The domain is all of the values of #x# for which the function exists. This function exists for all values of #x#, as it's a linear function; there is no value of #x# which would cause division by #0# or a vertical asymptote, a negative even root, a negative logarithm, or any situation which would cause the function to not exist. The domain is #(-∞,∞)#. The range is the values of #y# for which the function exists, in other words, the set of all possible resulting #y# values obtained after plugging in #x#. By default, the range of a linear function whose domain is #(-∞,∞)# is #(-∞,∞)#. If we can plug in any #x# value, we can obtain any #y# value.

Hazel Anglin · Answer

#x in R#- x can take any real value
#y in R#- y can take any real value

If you image the function as #y=2(x-3)# we can model it as a graph, which should make it more clear. The graph indicates that both x and y extend to infinity, which implies that it spans all possible values of x, all possible values of y, and all of their fractions. Although the graph shows that all real values are acceptable answers, the domain is about "Which x values can or cannot my function take?" and the range is the same but for the y values the function can or cannot take. graph{y=2(x-3) [-5, 5, 10, 10, 5]}

Nathan Axel · Answer

Because there are no x values for which a y value does not exist, the domain is all real numbers. The range is also all real numbers.

A function's domain consists of all possible x values that cover the solution set; functions like radical and rational functions, which have the potential for a domain error, are the sources of domain discontinuities. In a rational function (ex. #5/(x-2)#) the denominator can not be equal to zero. This is because you cannot divide by zero, it produces a domain error. So when stating the domain of this given function, you may use all possible values of x where the denominator does not equal zero (x | x != 2) In a radical function (ex. #sqrt(x+4)#) the contents inside the square root cannot be equal to a negative number. This is because there are no real positive numbers which multiplied by themselves is equal to a negative number. Therefore, the domain of the function is all possible values of x where the root is positive (x | x>=-4). (note: for radical functions with an odd root, such as cube roots or 5th roots, negative numbers are within the solution set) While there are other functions that can result in domain errors, these two are the most frequently occurring in algebra. A function's range is its entire range of possible y values, which can be found by examining the function's graph. Looking at the graph of #x^2#, we can see that as the x values stretch to infinity, there are no negative y values. In other words, the graph never dips below the line y = 0. The range for this function is y | y >= 0) The best method to determine a function's range if you're not sure what it is is to examine the graph and note the upper and lower bounds of the y values.

Kennedy Adams · Answer

undefined To find the domain and range of the function 2(x-3), we consider the possible values of x and the resulting values of the function.

Domain: The domain of the function is all real numbers since there are no restrictions on the input values of x.

Range: The range of the function is also all real numbers because the function is a linear function, and its output can take on any real value depending on the input x.