what is the domain, range, and zeros of the function:
g(t)= root 9-t?
Can you have a root of a negative number? So that limits -inf<t <=9
thanks!
To find the domain, range, and zeros of the function g(t) = √(9 - t), we can follow these steps:
1. Domain:
The domain of a function refers to the set of all possible input values (t) for which the function is defined. In this case, the function involves a square root of (9 - t). For the square root to be defined, the expression inside the square root (9 - t) must be greater than or equal to zero. So, we set up the inequality: 9 - t ≥ 0.
Solving this inequality:
9 ≥ t.
Therefore, the domain of the function g(t) = √(9 - t) is all real numbers t such that t ≤ 9.
2. Range:
The range of a function refers to the set of all possible output values. Since the square root function always gives a non-negative result, the range of the function g(t) = √(9 - t) will be all non-negative real numbers.
So, the range is: Range (g) = [0, ∞).
3. Zeros:
The zeros of a function are the values of t that make the function equal to zero. In this case, we need to solve the equation √(9 - t) = 0.
Squaring both sides, we get:
9 - t = 0.
Solving this equation, we find t = 9.
Therefore, the zeros of the function g(t) = √(9 - t) is t = 9.
g(t)=√(9-t)
zero: (9,0)
domain: x can be all real numbers less than or equal to 9
range: y can be all real numbers greater than or equal to 0