A wildlife had 8 elephant calves born during the summer and now has 31 total elephants. How many elephants were in the reserves
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Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.
<h3>What is the Factor Theorem?</h3>The Factor Theorem states that a polynomial function with roots is given by:
In which a is the leading coefficient.
Considering the table, the roots are given as follows:
Hence the function is:
f(x) = a(x + 4)(x - 5)(x - 12).
f(x) = a(x² - x - 20)(x - 12)
f(x) = a(x³ - 13x² - 32x + 240).
When x = 0, y = 1, hence the leading coefficient is found as follows:
240a = 1
a = 0.004167
Then:
f(x) = 0.004167(x³ - 13x² - 32x + 240).
The end behavior is given by the limits of f(x) as x goes to infinity, hence:
.
.
Hence the end behavior is that the function decreases to the left and increases to the right.
More can be learned about the Factor Theorem at brainly.com/question/24380382
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