Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
to which there corresponds more than one value of y.
-xy + 3y = 5
A) A function with domain all real numbers except x = -3

Question

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x
 to which there corresponds more than one value of y.
-xy + 3y = 5
A) A function with domain all real numbers except x = -3

Quizplus · Accepted Answer

To determine if the equation specifies a function with independent variable x, we need to solve for y and check if there is more than one y value for a given x value.

xy + 3y = 5

Factor out y:

y(x+3) = 5

Solve for y:

y = 5/(x+3)

This equation specifies a function with independent variable x because for every value of x, there is only one corresponding value of y.

However, the denominator (x+3) cannot be equal to 0 because division by 0 is undefined. Therefore, the domain of the function is all real numbers except x = -3 (since that would make the denominator 0).

So the answer is A, a function with domain all real numbers except x = -3. This equation specifies a function with independent variable x because for every input value of x, there is only one corresponding output value of y. To find the domain, solve for y:
xy + 3y = 5
y(x + 3) = 5
y = 5 / (x + 3)
The only restriction for the domain is that the denominator (x + 3) cannot be equal to 0, so x cannot equal -3. Therefore, the domain is all real numbers except x = -3.

Determine If the Equation Specifies a Function with Independent Variable