Use the leading coefficient and degree of the polynomial function f(x) = x3 – 7x2 + 10x to determine the end behavior of its graph. Select all the correct statements. A. As x → ∞, y → ∞. B. As x → ∞, y → −∞. C. As x → −∞, y → ∞. D. As x → −∞, y → −∞. E. As x → ∞, y → 0.

We want to study the end behavior of the given polynomial.

The two correct statements are A and D.

The polynomial is:

f(x)  = x^3 - 7*x^2 + 10*x.

We can see that the degree of this polynomial is odd, this means that the behavior on the negative side is opposite to the one in the positive side.

In this case, the leading coefficient is one, so it is positive. This will mean that, for large positive values of x, f(x) will be positive.

For large (in absolute value) negative values of x, f(x) will be negative.

Then the end behavior is given by:

So the two correct statements are A and D.

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Given:

The function is

To find:

The end behavior of its graph.

Solution:

We have,

Here, leading coefficient is 1 which is positive and degree of function is 3 which is odd.

For odd degree and positive leading coefficient, the end behavior is

Using this, we get

Therefore, the correct statements are A and D.

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