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)
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Evaluate the integral.
A. 3i + 
j + 4(1 + 
)k
B. 3i + 
j + 4(1 - 
)k
C. 3i + 
j + 4(1 + 
)k
D. 3i + 
j + 4(1 - 
)k
Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema.f(x) = x5 - 15x4 - 3x3- 172x2 + 135x + 0.04
A. Approximate local maximum at 0.439; approximate local minimum at -12.663 B. Approximate local maximum at 0.379; approximate local minimum at 12.565 C. Approximate local maximum at 0.332; approximate local minima at -0.517 and -12.508 D. Approximate local maximum at 0.379; approximate local minima at -0.472 and 12.565
Provide an appropriate response.The series of sketches below starts with an equilateral triangle having sides of length 1 (one). In the following steps, equilateral triangles are constructed by joining the midpoints of the sides of the preceding triangle. Develop a formula for the area of the nth new triangle. Use math induction to prove your answer.
What will be an ideal response?
Graph the line that passes through the point (-1, -2) and has slope  figure 1.png)
 figure 2.png)
 figure 3.png)
 answer.png)