Final answer:
The function f(x) = (x²+4x-12)/(x+6) simplifies to a straight line f(x) = x - 2 with a slope of 1 after factoring and cancelling out like terms, but it is undefined at x = -6, due to the hole in the graph.
Step-by-step explanation:
The graph of the function f(x) = \frac{x^2+4x-12}{x+6} is not straightforward to determine without some analysis. First, we identify that this function is a rational function and not a polynomial like a parabola, cubic function, or a straight line. Simplifying the function, if possible, can help us better understand its characteristics. If we factor the numerator, we get (x+6)(x-2). Notice that the (x+6) in the numerator and denominator will cancel out, leaving us with f(x) = x - 2 for all x \\eq -6.
Therefore, the graph of this equation is a straight line with a slope of 1 and a y-intercept at -2, except for a hole at x = -6 where the function is undefined. This matches none of the options exactly, but the closest incorrect answer from the provided options is (b) A straight line with a slope of 1. The student should be aware of the exception where the denominator causes undefined points in the function.