What is the graph of the function f(x) = the quantity of x squared plus 3 x plus 5, all over x plus 2

I assume you are asking f(x) = (x^2 + 3x + 5) / (x+2)

Let's assume g(x) = x^2 + 3x + 5 = (x+2)^2 + (1-x)

Therefore, f(x) = g(x) / (x+2) = (x+2) + (1-x) / (x+2)

Let x+2 = t

Then f(t) = t + (3-t) / t = t + 3/t - 1, where t ≠ 0

Therefore, the graph is shown in the first attachment.

Since t = x + 2

Your final graph will be 2 units shifted to the left of f(t), which is the second graph:

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4