The domain of a function represents all possible input values (x-values) for which the function is defined, while the range represents all possible output values (y-values) that the function can take.
For the given function, y = -|x| + 1, the domain can be any real number since the absolute value function can take any value as input.
Domain: All real numbers, (-∞, ∞)
To find the range, we need to consider the possible values of y. The absolute value of any number is always greater than or equal to zero, so the negative of the absolute value will always be less than or equal to one.
However, since it is possible to get arbitrarily close to 1 by taking a large negative value of x, the range of the function is from negative infinity to 1.
Range: (-∞, 1]