Determine if x2+y2=9

Question

is a function by graphing.

Answer 1

To determine if x^2 + y^2 = 9 is a function, we can graph it and check if it passes the vertical line test.

First, we rearrange the equation to solve for y: y = sqrt(9 - x^2).

Now, we can substitute different values of x into the equation to find the corresponding y values and graph the points.

When x = 0, y = sqrt(9 - 0^2) = 3, so we have the point (0, 3).
When x = 1, y = sqrt(9 - 1^2) = sqrt(8), so we have the point (1, sqrt(8)).
When x = -1, y = sqrt(9 - (-1)^2) = sqrt(8), same as when x = 1, so we have the point (-1, sqrt(8)).
When x = 2, y = sqrt(9 - 2^2) = sqrt(5), so we have the point (2, sqrt(5)).
When x = -2, y = sqrt(9 - (-2)^2) = sqrt(5), same as when x = 2, so we have the point (-2, sqrt(5)).

Plotting these points on the graph, we can see that they lie on a circle centered at the origin with a radius of 3.

The graph appears as a vertical line test. Any vertical line will intersect the circle at two points, indicating that x^2 + y^2 = 9 is not a function.

Therefore, x^2 + y^2 = 9 is not a function.