The function that plots a graph is given from the characteristics of the graph
The option that gives the function that could possibly have created the graph is the option;
- D. F(x) = x⁴ - x³ - 3·x² + 3
Reason:
- The graph is U-shaped, therefore, the leading coefficient is, a > 0
Therefore; Options (A) and (B) could not have created the graph
- The graph does not have a zero at the origin
Therefore; Option (C) f(x) = x⁵ + 13·x⁴ + 12·x = x·(x⁴ + 13·x³ + 12) could not have created the graph because, x = 0 is not a factor
Which gives;
The function which could possibly create the graph is the option;
D. F(x) = x⁴ - x³ - 3·x² + 3 = (x - 1)·(x³ -3·x - 3)
- The leading coefficient is 1 > 0
- The function has no factors of x = 0
- The function has a linear factor
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