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 + 2)

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, 0), x-intercepts: (0, 0) and (-2, 0)
(c) The graph of f crosses the x-axis at (-2, 0) and touches the x-axis at (0, 0).
(e) Local minimum at (0, 0), Local maximum at (-1.33, 1.19)
(f)

(g) Domain of f: all real numbers; range of f: all real numbers
(h) f is increasing on (-?, -1.33) and (0, ?); f is decreasing on (-1.33, 0)

Mathematics

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Four players (Alli, Blake, Corey, and Devin) are sharing a cake. Suppose that the cake is divided into four slices s1, s2, s3, and s4.To Devin, s1 is worth $2.70, s3 is worth $3.90, s2 and s4 have equal value, and the entire cake is worth $14.00. Determine which of the four slices are fair shares to Devin.

A. s2, s3, and s4 B. s1 and s2 C. s2 and s4 D. s1, s3, and s4 E. s3 and s4

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Mathematics