Question

Determine if the equation specifies a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y. x ^2+y^2 =144 Does the equation specify a function with independent value x ?

A. Yes
B. No

Answer 1

The equation x^2 + y^2 = 144 does not specify a function with the independent variable x. The equation represents a circle with a radius of 12, and there are two corresponding y-values for each x-value on the circle. Therefore, the answer is B.

Step-by-step explanation:

The equation x^2 + y^2 = 144 does not specify a function with the independent variable x. To determine if an equation represents a function, we need to check if each x-value corresponds to only one y-value. In this case, the equation represents a circle with a radius of 12, and for each x-value on the circle, there are two corresponding y-values.

The domain of a function is the set of all possible x-values. Since the equation does not represent a function, it does not have a domain.

To find a value of x that corresponds to more than one value of y, we can choose any x-value on the circle and calculate the corresponding y-values. For example, if we choose x = 0, we have y = 12 and y = -12.