Question

Consider the function f(x) = (x^2+x-12)/(x-3). Describe the graph of this function. Include all discontinuities, intercepts, and the basic shape of the graph.

Answer 1

Factor the numerator first, you'll notice the denominator will cancel out

Answer 2

factorise the numerator

f(x) = (x +4)(x-3)/(x-3)

the graph has a point of discontinuity at x = 3

you end up with the straight line y = x + 4

but put an open circle in the line at (3, 7) the point of discontinuity

y intercept y = 4, x intercept x = -4

Answer 3

Thank you!