Final answer:
The domain of the function y=6x−9 given the constraints is all real numbers greater than -15, and the range is all real numbers for y less than 27.
Step-by-step explanation:
The student has asked about the domain and range of the function y=6x−9 given the constraints that x-values are greater than −15 and y-values are less than 27. To find the domain, we consider the given constraint for x: since the function is defined for x-values greater than -15, the domain is all real numbers greater than -15. To calculate the range, we plug the upper limit of y into the equation and solve for x to find the maximum value of x that will give us a value of y less than 27.
Let's find the maximum x-value:
27 = 6x - 9
Add 9 to both sides:
27 + 9 = 6x
36 = 6x
Divide both sides by 6:
x = 6
So, the maximum value of x that will keep y under 27 is 6. Therefore, the domain of the function is x > -15, and the range of the function is y < 27.