The function T(x)=0.25(x-4400)+440 represents the tax bill T
of a single person whose adjusted gross income is x
dollars for income between
$4400 and $17,600 inclusive. (a) What is the implied domain of the linear function? (b) What is a single filer's tax bill if adjusted gross income is
$10,000? (c) Which variable is independent and which is dependent? (d) Graph the linear function over the domain specified in part (a).
(e) What is a single filer's adjusted gross income if the tax bill is $1440?
(a) The implied domain of the linear function T(x) is the range of values for which the function is defined and meaningful. In this case, the function is defined for income between $4400 and $17,600 inclusive, so the implied domain is x ∈ [4400, 17600].
To get the implied domain, you need to look at the given representation of the function and determine which values of x would make sense to plug in.
(b) To find a single filer's tax bill if their adjusted gross income is $10,000, you can substitute x = 10000 into the function T(x) and evaluate it.
T(x) = 0.25(x - 4400) + 440
T(10000) = 0.25(10000 - 4400) + 440
By simplifying this expression, you can calculate the tax bill.
(c) In the given function T(x) = 0.25(x - 4400) + 440, x represents the adjusted gross income, while T(x) represents the tax bill. The dependent variable is the tax bill (T(x)) because it depends on the value of the independent variable, adjusted gross income (x).
(d) To graph the linear function, you can plot points on a graph using different values of x within the implied domain and then connect them with a straight line.
For example, you can choose minimum and maximum values from the implied domain, like x = 4400 and x = 17600. Substitute these values into the function and plot the corresponding points (4400, T(4400)) and (17600, T(17600)). Connect these two points with a straight line to represent the linear function.
(e) To find a single filer's adjusted gross income if the tax bill is $1440, you can set T(x) = 1440 in the function and solve for x.
1440 = 0.25(x - 4400) + 440
By rearranging this equation and solving for x, you can determine the adjusted gross income.