Given the function y = square root of 6x +9 What is the domain of the function?
Hint: Look at the x values when you graph the function in Desmos.
You may use interval notation or inequalities for your answer.
The expression under the square root sign must be non-negative for real values of x, otherwise the function is undefined. Therefore, we must solve the inequality 6x + 9 ≥ 0.
Subtracting 9 from both sides, we get 6x ≥ -9, and dividing both sides by 6 results in x ≥ -3/2.
Therefore, the domain of the function is x ≥ -3/2, or in interval notation, (-3/2, ∞).
To determine the domain of the function y = √(6x + 9), we need to consider the values that x can take.
Since we're dealing with the square root of a quantity, the expression inside the square root (6x + 9) must be greater than or equal to zero.
6x + 9 ≥ 0
Subtracting 9 from both sides:
6x ≥ -9
Dividing both sides by 6:
x ≥ -9/6
Simplifying the fraction:
x ≥ -3/2
So, the domain of the function can be expressed in interval notation as:
(-3/2, ∞)