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) = -x2(x - 1)(x + 3)
What will be an ideal response?
(a) For large values of |x|, the graph of f(x) will resemble the graph of y = -x4.
(b) y-intercept: (0, 0), x-intercepts: (-3, 0) , (0, 0), and (1, 0)
(c) The graph of f crosses the x-axis at (1, 0) and (-3, 0) and touches the x-axis at (0, 0).
(e) Local maxima at (-2.19, 12.39) and (0.69, 0.55); Local minimum at (0, 0)
(f) 
(g) Domain of f: all real numbers; range of f: (-?, 12.39]
(h) f is increasing on (-?, -2.19) and (0, 0.69); f is decreasing on (-2.19, 0) and (0.69, ?)
You might also like to view...
Solve the problem.A certain store has a fax machine available for use by its customers. The store charges $2.05 to send the first page and $0.60 for each subsequent page. Use an inequality to find the maximum number of pages that can be faxed for $10.45
A. at most 55 pages B. at most 17 pages C. at most 14 pages D. at most 5 pages
Solve the problem.Rounded to three decimal places, the two solutions of x2 = x + 1 are
A. 1.618 and -1.618. B. 1.618 and -0.618. C. 1.618 and 2.236. D. 1.618 and 0.618. E. none of these
Solve the inequality graphically. Give the solution in interval notation.Use the intersection method to solve -11x - 8 ? -12x - 6.
A. [2, ?) B. (-?, 2] C. (-?, -11) D. (-11, ?)
Sketch the region enclosed by the curves 
and x = 2. Find the area of the region correct to two decimal places.
What will be an ideal response?