The polynomial function represented by the data is equal to D. f(x) = −x² + 10.
In order to determine the polynomial function represented by the data, we would substitute the value of x (-3) into the given set of functions as follows:
For option A, we have:
f(x) = 6x + 15
f(-3) = 6(-3) + 15
f(-5) = -18 + 15
f(-5) = -3 (False).
For option B, we have:
f(x) = -6x - 45
f(x) = -6(-3) - 45
f(x) = 18 - 45
f(x) = -27 (False).
For option C, we have:
f(x) = x² - 40
f(x) = -3² - 40
f(x) = 9 - 40
f(x) = -31 (False).
For option D, we have:
f(x) = −x² + 10
f(x) = −(-2)² + 10
f(x) = −9 + 10
f(x) = 1 (True).
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Complete Question:
A polynomial function is represented by the data in the table.
x = -5, -4, -3, -2, -1
f(x) = -15, -6, 1, 6, 9
Choose the function represented by the data.
A. f(x) = 6x + 15
B. f(x) = −6x − 45
C. f(x) = x² − 40
D. f(x) = −x² + 10
