Final answer:
The function g(x)=2|x| has a domain of all real numbers and a range of all non-negative real numbers. The graph is a V-shaped curve symmetric about the y-axis with the vertex at the origin (0,0).
Step-by-step explanation:
Graphing the function g(x)=2|x| involves plotting the function's value over the range of x values that you are interested in. The domain of a function refers to all the possible input values (x values) for which the function is defined, and the range refers to all the possible output values (y values) the function can take on.
In the case of g(x)=2|x|, the domain is all real numbers, since you can take the absolute value of any real number. The range, however, is all non-negative real numbers since the absolute value always returns a non-negative number, and multiplying by 2 still keeps it non-negative.
To graph this function, you would plot points where the y-value is twice the absolute value of the x-value. This will result in a V-shaped graph with its vertex at the origin (0,0) because the function equals zero when x is zero. This graph will be symmetric with respect to the y-axis, since the absolute value of x is the same for both positive and negative x values, just multiplied by 2.