Question

Pls I am really struggling here

How do you know the end behavior of a polynomial function if the first number is a variable? Do you just move on to the next term that is a number

Answer 1

Yeah your right

Explanation:

Answer 2

You need to bring the function to the standard form.

The term with highest degree exponent is the leading term and its coefficient is the leading coefficient.

Let it be axⁿ.

Depending on the n and a, the end behavior of the function will change.

Case 1

• a > 0, n - is odd

This is an odd function and:

• x → -∞ ⇒ f(x) → -∞
• x → ∞ ⇒ f(x) → ∞

Case 2

• a < 0, n - is odd

This is an odd function and:

• x → -∞ ⇒ f(x) → ∞
• x → ∞ ⇒ f(x) → -∞

Case 3

• a > 0, n - is even

This is an even function and:

• x → -∞ ⇒ f(x) ⇒ ∞
• x → ∞ ⇒ f(x) ⇒ ∞

Case 4

• a < 0, n - is even

This is an even function and:

• x → - ∞ ⇒ f(x) ⇒ - ∞
• x → ∞ ⇒ f(x) ⇒ - ∞