END BEHAVIOR OF A POLYNOMIAL FUNCTION WORKSHEET

Answer Key

1)

 f(x) = x⁴ - x² + 5x - 4

Degree of the polynomial f(x) is 4, it is even.

a = 1  > 0

The function f(x) is even degree with positive leading coefficient on its dominating term. It exactly matches with graph C.

g(x) = -x⁶ + x² - 3x - 4

Degree of the polynomial f(x) is 6, it is even.

a = -1  < 0, then as | x | -> ∞, P(x) -> -∞. Option A is correct.

h(x) = 3x³ - x² + 2x - 4

h(x) is the polynomial of odd degree and a = 3 > 0

When x -> ∞, P(x) -> ∞ and as x -> -∞, P(x)  -> -∞. So, option B is correct.

k(x) = -x⁷ + x - 4

h(x) is the polynomial of odd degree and a = -1 < 0

When | x | -> ∞, P(x) -> -∞. So, option D is correct.

2)

f(x) = 2x³ + x² - x + 3

f(x) is the odd degree polynomial, here a = 2 > 0

When x -> ∞, P(x) -> ∞ and as x -> -∞, P(x)  -> -∞. So, option D is correct.

g(x) = - 2x³ - x + 3

g(x) is the odd degree polynomial, here a = -2 < 0

When | x | -> ∞, P(x) -> -∞. So, option C is correct.

h(x) = -2x⁴ + x³ - 2x² + x + 3

It is even degree polynomial. Here a = -2 < 0

When | x | -> ∞, P(x) -> -∞. So, option B is correct.

k(x) = 2x⁴ - x³ - 2x² + 3x + 3

It is even degree polynomial. Here a = 2 > 0

When | x | -> ∞, P(x) -> ∞. So, option A is correct.