if the domain of the function y=|x| is the set of all real numbers, what is the range of the function?

Question

a) all real numbers
b) all non-negative real numbers
c)all rational numbers
d) all non-negative rational numbers
please include explanation thank you very much

Answer 1

B. all non negative real #'s
The range applies to where the function lives corresponding to the y axis... since it only lives above zero (since its lxl and it cant be negative!! ) we know that the range is all NON neg. real #'s.

Answer 2

b), because if x is a real number, then |x| always returns a non-negative real number. It can't be "all real numbers" because -1 is a real number, and there's no value of x for which |x|= -1. And it's not "all rational numbers" for the same reason. Nor is it "all non-negative rational numbers", because √2 is a real number but not rational, and |√2| = √2.

Answer 3

For every real x, |x| is x, if x >=0 and -x if x <0. This is the absolute value function. Therefore, |x| >0 if x diffrenet from 0 and |0| = 0.

It follows the answer is the set of all non-negative real numbers, (c)

Answer 4

Range means what values of y can the function have? So to get that, you ask yourself, since you know the domain, what values of y can you get and which can you not get? Since the absolute value function just takes the x value and essentially makes it positive if it is not already, the range is all numbers greater than or equal to 0, written [0,infinity) or 0<=x

Answer 5

The domain for all these is all real numbers. The range of 1. is y>=0 since absolute value is alway >=0 Similarly the range of 2 is y>=0 In 3. we have abs(x)>=0 so abs(x)-3>=-3 or y>=-3 In 4. since abs>=0, -abs<=0 so y<=0 ..

Answer 6

b) all non-negative real numbers. The range (y) is equal to the absolute value of (x) the domain.

Answer 7

b) In taking the absolute value, you are simply converting negative reals to positive and leaving positive reals alone.

Answer 8

could be a few kilometers....but I doubt its accuracy. So where's the catch?