Answer:
To determine the domain and range of the function y = |x - 2| + 1, we need to consider the restrictions on the input values (x) and the resulting output values (y).
Domain:
The domain refers to the set of all possible input values (x) for the function. In this case, since the absolute value function can accept any real number as input, there are no restrictions on the domain. Therefore, the domain is all real numbers (-∞, +∞).
Range:
The range refers to the set of all possible output values (y) for the function. For the given function, y = |x - 2| + 1, the absolute value function ensures that the output (y) is always non-negative. Additionally, the "+ 1" term in the function shifts the graph upward by 1 unit. Therefore, the range of this function is all real numbers greater than or equal to 1 ([1, +∞)).
In summary:
Domain: All real numbers (-∞, +∞)
Range: All real numbers greater than or equal to 1 ([1, +∞))
#Hope it helps :)
