Answer: right side = as x → ∞, y → -∞ & left side = as x → -∞, y → -∞
<u>Step-by-step explanation:</u>
To find end behavior, we need to evaluate 2 things: Sign of the leading coefficient and Degree of the function.
Sign: Determines the end behavior of the right side.
- Positive: right side goes to positive infinity
- Negative: right side goes to negative infinity
Degree: Determines the end behavior of the left side
- Odd: left side is opposite of right side
- Even: left side is same as right side
f(x) = -4x⁶ + x² - 52
1. Sign is negative so right side goes to negative infinity (as x → ∞, y → -∞)
2. Degree is even so left side is the same as right side so it also goes to negative infinity (as x → -∞, y → -∞)
-52