The domain is: [18,∞),{x|x≥18}
The range is: [0,∞),{y|y≥0}
The range is: [0,∞),{y|y≥0}
y = 1 - 1/(2√(3x-6))
I get a horizontal asymptote at y=1, with the range (-∞,1)
We have the equation: 2(y-1) = -√(1/3x-6)
First, eliminate the coefficient of 2 by dividing both sides of the equation by 2:
(y-1) = -√(1/3x-6) / 2
Next, isolate y by adding 1 to both sides of the equation:
y = 1 - √(1/3x-6) / 2
Now that we have solved for y, we can determine its range. The range represents all the possible values that y can take. In this case, the square root function (√) can only produce non-negative values, so the expression inside the square root (1/3x-6) must be non-negative.
1/3x-6 ≥ 0
To solve for x, multiply both sides of the inequality by 3:
1 ≥ 3(1/3x-6)
Now, distribute the 3 on the right side:
1 ≥ x - 18
Add 18 to both sides:
19 ≥ x
Therefore, the domain for this equation is x ≤ 19.
Lastly, let's consider the range. Since we've determined that the expression inside the square root (1/3x-6) must be non-negative, it means that the square root (√) is always positive or zero. Therefore, the range for y is y ≥ 1.
In summary, the domain is x ≤ 19, and the range is y ≥ 1.