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) = -2(x - 2)(x + 2)3
What will be an ideal response?
(a) For large values of |x|, the graph of f(x) will resemble the graph of y = -2x4.
(b) y-intercept: (0, 32), x-intercepts: (-2, 0) and (2, 0)
(c) The graph of f crosses the x-axis at (2, 0) and crosses the x-axis at (-2, 0).
(e) Local maximum at (1.00, 54.00)
(f) 
(g) Domain of f: all real numbers; range of f: (-?, 54.00]
(h) f is increasing on (-?, -2) and (-2, 1.00); f is decreasing on (1.00, ?)
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Find the gradient field of the function.f(x, y, z) = 
3
A. ?f = 
i + 
j - 3
k
B. ?f = 3
2i + 
j + 3
k
C. ?f = 3
2i + 
j - 3
k
D. ?f = 3
2i + 
j + 3
k
Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply.
i
A. complex, pure imaginary B. real C. real, complex D. complex, nonreal complex
Use transformations of the graphs of y = x2 or y = |x| to sketch a graph of f by hand.f(x) = 5x2 + 5 
A. 
B. 
C. 
D. 
Solve the problem.If x dollars is deposited every four weeks (13 times a year) into an account paying an annual interest rate r, expressed in decimal form, then the amount An in the account after n years can be approximated by the formula 
If 
is deposited every four weeks into an account paying 
interest, approximate the amount in the account after 16 years.
A. $9532.60 B. $16,146.00 C. $317.75 D. -$4300.64