Question

What can you say about the nd behavior of the function f(x)=-4tle="x^{6}" alt="x^{6}" align="absmiddle" class="latex-formula">+$x^{2}$-52

Answer 1

Answer: right side = as x → ∞, y → -∞  & left side = as x → -∞, y → -∞

Step-by-step explanation:

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 → -∞)