Final answer:
The function f(x) = (2x^2 + 5x - 3) / (x + 3) has a discontinuity at x = -3, which is where the function is undefined because the denominator is zero.
Step-by-step explanation:
The student has asked to investigate the discontinuity of the function f(x) = (2x^2 + 5x - 3) / (x + 3). Discontinuities occur where the function is undefined, which, for rational functions, is often where the denominator is zero. Since our denominator is (x + 3), setting it equal to zero, x + 3 = 0, we find that x = -3 is the point of discontinuity. Therefore, the function is undefined at x = -3, leading to a discontinuity at this point.