Answer:
As x → - ∞ , y → - ∞ and as x→ ∞ , y → -∞
<h3>
option B is the correct option.</h3>
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.
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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!!
