Question

(4/4) PLEASE HELP! URGENT.. LAST QUESTION. WILL MARK BRAINLIEST AND 5 STARS IF CORRECT ASAP! -50POINTS-

Answer 1

Answer:

As x → - ∞ , y → - ∞ and as x→ ∞ , y → -∞

option B is the correct option.

Step-by-step explanation:

f ( x ) = - 5x⁴ + 7x² - x + 9

Here, dominating term is ( -5x⁴ ) which has even exponent.

Now, as x → ∞ ⇒ - 5x ⁴⇒ - ∞ [ x⁴ → ∞ ]

⇔ f (x) → - ∞ [ -5x⁴ is dominating term ]

x→ ∞ , y → -∞

as x→ - ∞ , ( -5x⁴ ) → - ∞ [ x⁴ → ∞ ]

as x→ - ∞ , y → -∞

Hence, Option B is the correct option.

------------------------------------------------------------------

You just have to focus on leading term, which is the term that has highest exponent of variable, as in our case , it is -5x⁴.

And then find leading coefficient, whether it is positive or negative degree ( power of variable) and whether it is even number or odd number)

Then, if leading coefficient is negative and degree is positive then always y will approach -∞ .

Hope this helps...

Best regards!!

Answer 2

Answer:

As x goes to negative infinity, y goes to  - ∞

As x goes to infinity, y goes to  - ∞

Step-by-step explanation:

We need to look at the dominate term

-5x^4

As x goes to negative infinity

-5 *(- ∞) ^ 4 = -5 * ∞ = - ∞

As x goes to negative infinity, y goes to  - ∞

As x goes to  infinity

-5 *( ∞) ^ 4 = -5 * ∞ = - ∞

As x goes to infinity, y goes to  - ∞