# What is the domain and range of y=|x-3|+2?

domain and range

The function is y = | x - 3| + 2.

Domain of the function is the set of all real numbers.

Since, | x - 3 | is either positive or zero for x = 3, the range of the function is given by the interval [0,  infinity].

The function is y = | x - 3| + 2.

The value of | x - 3 | is either positive or zero.

If | x - 3 | is positive then y = positive value + 2 -----> y > 2.

If | x - 3 | is zero then y = 0 + 2 -----> y = 2.

Range is  y ≥ 2.

The function is y = | x - 3| + 2.

The function y = | x - 3| + 2 is an absolute value function.There are no rational or radical expressions, so there is nothing that will restrict the domain. Any real number can be used for x to get a meaningful output.

So, the domain of the function is the set of all real numbers.

The function y = | x - 3| + 2 is the transformation function and its parent function is f(x) = | x |.

The range of parent function is f(x) ≥ 0.

Compare the graph of y = | x - 3| + 2 with the graph of f(x) = | x | :

The graph of y is a right shift of three units followed by a upward shift of two units of the graph of f(x).

y = | x - 3| + 2 = f(x - 3) + 2.

Therefore  y - value shifted from 0 to 2.

The range of y = | x - 3| + 2 is y ≥ 2.