Analyze the graph of the given function f as follows:(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.(b)  Find the x- and y-intercepts of the graph.(c)  Determine whether the graph crosses or touches the x-axis at each x-intercept.(d)  Graph f using a graphing utility.(e)  Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.(g)  Find the domain of f. Use the graph to find the range of f.(h)  Use the graph to determine where f is increasing and where f is decreasing.f(x) = 

src="https://sciemce.com/media/4/ppg__10624191726__f1q156g1.jpg" style="vertical-align: -17.0px;" />x3 - x2 - 3x + 15



What will be an ideal response?

---

(a) For large values of |x|, the graph of f(x) will resemble the graph of y = x³.
(b) y-intercept: (0, 15), x-intercepts: (-3, 0), (3, 0), and (5, 0)
(c) The graph of f crosses the x-axis at each of the intercepts (-3, 0), (3, 0), and (5, 0).
(e) Local maximum at (-0.74, 16.17); Local minimum at (4.07, -2.35)
(f) 

(g) Domain of f: all real numbers; range of f: all real numbers
(h) f is increasing on (-?, -0.74) and ; f is decreasing on (-0.74, 4.07)

Mathematics