To determine the type of function depicted by the table, we need to analyze the relationship between the input values (x) and the output values (f(x)). The table is as follows:
| x | f(x) | |-----|-------| | -2 | -3 | | -1 | -38 | | 0 | -133 | | 1 | -318 | | 2 | ? |
To identify the type of function, look for patterns.
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Identify the differences: Calculate the differences between consecutive f(x) values:
- From -3 to -38: \(-38 - (-3) = -35\)
- From -38 to -133: \(-133 - (-38) = -95\)
- From -133 to -318: \(-318 - (-133) = -185\)
The differences (-35, -95, -185) do not seem constant but let's check the second differences:
- From -35 to -95: \(-95 - (-35) = -60\)
- From -95 to -185: \(-185 - (-95) = -90\)
Since the second differences are not constant either (they are -60 and -90), this suggests that the relationship may not be quadratic.
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Check for polynomial degree: Given that neither first nor second differences offer a constant change, the behavior of the output values suggests that this function may be of a higher degree polynomial or an exponential function.
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Observations: The output values are decreasing rapidly, indicating a possible exponential decay or a polynomial function with a negative leading coefficient.
Conclusion
This function is likely a polynomial function of degree greater than 2, given the non-linear output pattern observed with the inputs. Since the differences do not stabilize into a clear pattern, we can imply that function does not fit typical linear or quadratic forms cleanly and could be of a higher degree.
Answer: This function is likely a polynomial function of degree greater than 2 because the differences in output values are not consistent enough to suggest it is linear or quadratic.
3 answers