Find the domain and range of y= |2x| + 2 ?

The domain of the function y = |2x| + 2 is all real numbers because there are no restrictions on the values that x can take.

To find the range of the function, we need to consider the possible values of |2x| + 2. Since the absolute value function always returns a non-negative value, the minimum value of |2x| is 0 when x = 0. Therefore, the minimum value of |2x| + 2 is 2 when x = 0.

As x increases or decreases, the value of |2x| will also increase. Therefore, the range of the function y = |2x| + 2 is all real numbers greater than or equal to 2, i.e., y ≥ 2.

Domain:

The domain of a function is the set of all possible input values. Since x can be any real number, the domain of y = |2x| is (-∞, ∞).

Range:

The range of a function is the set of all possible output values. Since |2x| is always non-negative, the range of y = |2x| is [0, ∞).