Step-by-step explanation:
The domain of a function are the values of that you can plug into the function
.
Values inside of a root must be non-negative, which means that must be greater than or equal to zero. We can set up an equation to find the domain:
With this, we know the domain of the function is .
The range of a function are the values that can have. Since the equation is a cube root, the value will always be non-negative, meaning the range of the function is
.
Answer:
This translates to "y is any real number such that it is 0 or larger".
The reasoning is that the result of any absolute value function is either 0 or positive. In other words, we'll never get a negative result of an absolute value function. This is due to how absolute value represents distance. Negative distance does not make sense.
So if y = |x-3| then y = 0 is the smallest output possible. We could have any positive output we want.
In terms of a graph (see below), the V shape is at the lowest point (3,0). The y coordinate is all we care about in terms of finding the range. So we see the lowest y value is y = 0.
