Question

What happens to the graph of y=2x^3+x^2−7x−6 as x heads toward ∞ and −∞?A. as x→∞, y→∞ as x→−∞, y→−∞B. as x→∞, y→∞ as x→−∞, y→∞C. as x→∞, y→−∞ as x→−∞, y→−∞D. as x→∞, y→−∞ as x→−∞, y→∞

Answer 1

A. as x→∞, y→∞ as x→−∞, y→−∞

Explanation:

Given the function:

`y=2x^3+x^2−7x−6`

In order to determine the end behavior of f(x), we use the leading coefficient test.

When using the Leading coefficient test, the following rule applies:

• When the ,degree is odd and the leading coefficient is positive,, the graph falls to the left and rises to the right.

,

• When the ,degree is odd and the leading coefficient is negative,, the graph rises to the left and falls to the right.

,

• When the ,degree is even and the leading coefficient is positive,, the graph rises to the left and right.

,

• When the ,degree is even and the leading coefficient is negative,, the graph falls to the left and right.

From the function, f(x):

• The degree of the polynomial = 3 (Odd)

,

• The leading coefficient is 2 (Positive)

Thus, using the 1st rule of the 4 given above, we have that as x→∞, y→∞ as x→−∞, y→−∞.

The correct option is A.