End Behavior of Polynomial Functions

In a polynomial function, what's the end behavior of odd degree and leading coefficient positive?

• Down, Down

• Up , Down

• Down, Up

• Up, Up

Answer explanation

For a polynomial of odd degree with a positive leading coefficient, the end behavior is that as x approaches negative infinity, the function goes down, and as x approaches positive infinity, the function goes up. Thus, the correct answer is Down, Up.

What is the end behavior of a polynomial with even degree and a negative leading coefficient?

• Up, Down

• Down, Up

• Down, Down

• Up, Up

Answer explanation

A polynomial with an even degree and a negative leading coefficient will fall to the bottom on both ends. Therefore, the end behavior is Down on the left and Down on the right, making the correct answer Down, Down.

Which of the following describes the end behavior of an odd degree polynomial with a negative leading coefficient?

• Up, Up

• Down, Down

• Up, Down

• Down, Up

Answer explanation

An odd degree polynomial with a negative leading coefficient will fall to the right and rise to the left. Thus, the end behavior is Down on the right and Up on the left, corresponding to the choice 'Up, Down'.

If a polynomial function has an even degree and a positive leading coefficient, what is its end behavior?

• Down, Up

• Up, Up

• Down, Down

• Up, Down

Answer explanation

A polynomial with an even degree and a positive leading coefficient rises on both ends. Therefore, its end behavior is Up, Up, which is the correct choice.

What's the end behavior for f(x)= x ( x + 5)^2?

• Down, Up

• Up, Down

• Down, Down

• Up, Up

Answer explanation

To determine the end behavior of f(x) = x(x + 5)^2, note that as x approaches -∞, f(x) approaches -∞ (down), and as x approaches +∞, f(x) approaches +∞ (up). Thus, the end behavior is Down, Up.

Identify the end behavior of f(x) = -x^2(x-2)^3(x+3).

• Down, Down

• Up, Up

• Down, Up

• Up, Down

Answer explanation

The leading term is -x^2, which is negative. As x approaches ±∞, f(x) will go to -∞. Thus, the end behavior is Down on both ends, confirming the correct choice is Down, Down.

What is the end behavior of odd degree polynomial functions?

• The ends point in opposite directions

• The graph is always a parabola

• The ends point in the same direction

• The graph is always a straight line

Answer explanation

Odd degree polynomial functions have end behavior where one end rises to positive infinity and the other falls to negative infinity, meaning the ends point in opposite directions. This is the correct choice.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the end behavior of even degree polynomial functions?

• The graph is always a parabola

• The ends point in opposite directions

• The graph is always a straight line

• The ends point in the same direction

Answer explanation

Even degree polynomial functions have end behavior where both ends of the graph point in the same direction, either upwards or downwards. This is why the correct answer is that the ends point in the same direction.

Tags

CCSS.HSF.IF.C.7

What's the end behavior of f(x)= -4 + (x - 3)^2?

• Down, Down

• Up, Up

• Down, Up

• Up, Down

Answer explanation

The function f(x) = -4 + (x - 3)^2 is a quadratic with a positive leading coefficient. As x approaches ±∞, (x - 3)^2 grows large, making f(x) approach +∞. Thus, the end behavior is Up, Up.

Tags

CCSS.HSF-IF.C.7A

What's the end behavior of f(x)=-x^2+6x-8?

• Down, Down

• Up, Up

• Down, Up

• Up, Down

Answer explanation

The function f(x)=-x^2+6x-8 is a downward-opening parabola (coefficient of x^2 is negative). As x approaches ±∞, f(x) approaches -∞. Thus, the end behavior is Down, Down.

Tags

CCSS.HSF-IF.C.7A