MATH SOLVE

3 months ago

Q:
# Which statement describes how the graph of the given polynomial would change if the term 2x5 is added?y = 8x4 – 2x3 + 5a. Both ends of the graph will approach negative infinity.b. The ends of the graph will extend in opposite directions.c. Both ends of the graph will approach positive infinity.d. The ends of the graph will approach zero.

Accepted Solution

A:

The original polynomial is

y =8x⁴ - 2x³ + 5

The modified polynomial, after adding 2x⁵, is

y = 2x⁵ + 8x⁴ - 2x³ + 5

Because the leading exponent is odd, therefore:

As x → -∞, y → -∞.

As x → +∞, y → +∞.

The graph confirms the conclusions.

Answer: b. The eds of the graph will extend in opposite directions.

y =8x⁴ - 2x³ + 5

The modified polynomial, after adding 2x⁵, is

y = 2x⁵ + 8x⁴ - 2x³ + 5

Because the leading exponent is odd, therefore:

As x → -∞, y → -∞.

As x → +∞, y → +∞.

The graph confirms the conclusions.

Answer: b. The eds of the graph will extend in opposite directions.