Answer:
Therefore, the end behavior of the function f(x) = −5x(x − 4)(x + 5)(2x + 3) is that it approaches negative infinity as x approaches positive infinity, and it approaches positive infinity as x approaches negative infinity.
Explanation:
The end behavior of a function refers to how the graph of the function approaches the x-axis as x approaches positive infinity or negative infinity.
To determine the end behavior of the function f(x) = −5x(x − 4)(x + 5)(2x + 3), we need to look at the signs of the factors and the leading coefficient for x as x approaches positive infinity and negative infinity.
As x approaches positive infinity, the leading term, -5x, dominates the other terms. The leading coefficient, -5, is negative, so the graph of the function approaches negative infinity.
As x approaches negative infinity, the term (x + 5) dominates the other terms. The coefficient of (x + 5), 1, is positive, so the graph of the function approaches positive infinity.
Therefore, the end behavior of the function f(x) = −5x(x − 4)(x + 5)(2x + 3) is that it approaches negative infinity as x approaches positive infinity, and it approaches positive infinity as x approaches negative infinity.