Complete the following:
(a)           Use the Leading Coefficient Test to determine the graph's end behavior.
(b)           Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.
(c)           Find the y-intercept. Show your work. f(x) = x^2(x + 2)

Question

Complete the following:
(a)           Use the Leading Coefficient Test to determine the graph's end behavior.
(b)           Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.
(c)           Find the y-intercept. Show your work.  f(x) = x^2(x + 2)

p0sitr0n · Answer

(a) Leading coefficient-> number multiplying the highest power of x, since it will determine the overall direction of the curve. Here its +1, hence f(x) will be O(x^3) in comp sci notation (asymptotically cx^3+lower terms). Remember that x^3 is positive over (0,+infty) and negative over (- infty, 0)