`f(x) = |2x|` Graph each function. Identify the domain and range.

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Chapter 2, 2.6 - Problem 30 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
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mrsgaboury | In Training Educator

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To graph the function f(x)=|2x| use a table of values or a graphing calculator, and note that the graph of an absolute value function is a piecewise function in the shape of a "v", in this case the two lines meet at zero:

To determine the domain and range of the function, recall the definitions of domain and range.  Briefly, domain is the input of the function--in this case, x.  Range is the output of the function--in this case, f(x).

Looking at the graph, see that the domain of the function is not limited, and extends through the entire range of real numbers along the x-axis.  Thus, the domain is expressed as:

{x} = all real numbers or -∞ < x < ∞

Again looking at the graph, it appears that the range of the function (along the y-axis) does not include any values less than zero.  Thus, the range can be expressed as:

f(x) ≥ 0

kspcr111's profile picture

kspcr111 | In Training Educator

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`f(x) = |2x|` , the the domain and range is given as follows

(i)Domain definition:

The domain of a function is the set of the input or argument values for which the function is real and defined.

In this function, the function has no undefined points, so the domain is 

`-oo <x<oo` .

(ii)Range definition

It is the  set of values of the dependent variable for which a function is defined. 

For this function the interval has a minimum point at x = 0 with value f(x) = 0

so the range of `|2x| is f(x) >= 0`

It can also be observed from the graph below:

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