Determine which viewing rectangle produces the most appropriate graph of the function. $$g ( x ) = 6 x ^ { 3 } - 15 x ^ { 2 } + 4 x - 1$$
A) $[ - 2,2 ]$ by $[ - 2,2 ]$
B) $[ - 8,8 ]$ by $[ - 8,8 ]$
C) $[ - 4,4 ]$ by $[ - 12,12 ]$
D) $[ - 100,100 ]$ by $[ - 100,100 ]$
E) $[ - 10,10 ]$ by $[ - 100,100 ]$

Question

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Since the degree of the function is odd (3) and the leading coefficient is positive, the ends of the graph go up to the left and up to the right. Therefore, we need a viewing window that extends farther out on the x-axis than it does on the y-axis. Option A is too small to see the ends of the graph, option B is too large to see the behavior of the function near the origin, option D and E are much larger than necessary and may make it difficult to see the details of the graph. Option C provides a good balance between seeing the details of the graph and seeing the behavior of the function as x approaches infinity and negative infinity.

Determine Which Viewing Rectangle Produces the Most Appropriate Graph of the Function