y= the square root of x+33......does this define y as a function of x?
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Um what does that mean....learn english
To determine whether the equation y = √(x+33) defines y as a function of x, we need to assess if for each input value of x, there is a unique output value of y.
In this scenario, the equation y = √(x+33) does define y as a function of x. Here's why:
1. Domain: The expression inside the square root, (x+33), suggests that x can take any real value. However, since the square root of a negative number is undefined in the real number system, we need to ensure that x+33 is non-negative or zero. Hence, the domain is x ≥ -33.
2. Range: The square root of a non-negative number is always a non-negative number or zero. Therefore, the range of the function is y ≥ 0.
3. Unique Output: For each valid input value of x, the equation y = √(x+33) will provide a single, non-negative value for y. Therefore, there is a unique output value for every input value, satisfying the definition of a function.
Hence, the equation y = √(x+33) does define y as a function of x.