Question

Without using technology, describe the end behavior of f(x) = -3x^4 + 7x^2 - 12x + 13
A. Down on the left, down on the right
B. Down on the left, up on the right
C. Up on the left, down on the right
D. Up on the left, up on the right

Answer 1

Answer:

A. Down on the left, down on the right

Step-by-step explanation:

Let x be negative infinity

f(-∞) = -3 (-∞)^4+ 7(-∞)^2 - 12(-∞) + 13

f(-∞) = -3 (∞)^4+ 7(∞)^2 + 12(∞) + 13

The term that dominates is ∞^4

That term is negative because of the -3, so it goes down

f(∞) = -3 (∞)^4+ 7(∞)^2 - 12(∞) + 13

f(∞) = -3 (∞)^4+ 7(∞)^2 - 12(∞) + 13

The term that dominates is ∞^4

That term is negative because of the -3, so it goes down

It is down at -∞ and down and +∞