f(x)=-2x^2+14/x^2-49 which statement describes the behavior of the graph of the function shown at the vertical asymptotes?

Option 3 :

x → 7+, y → –[infinity]

Step-by-step explanation:

f(x) = (-2x² + 14)/(x² - 49)

x² - 49 = (x + 7)(x - 7)

Hence f(x) goes to infinity at x = - 7 or 7

x < - 7 = (-ve)(-ve) = + ve

=> x → –7–

Here, x² - 49 is + ve

-7 < x < 7 = (+ve)(-ve) = - ve

=> x → –7+ or x → 7– .

here, x² - 49 is - ve

x > 7 = (+ve)(+ve) = + ve

=> x → 7+

Here, x² - 49 is + ve

So (-2x² + 14) is - ve for all [ x → –7– , x → –7+ , x → 7– , x → 7+ ]

As,

-2(-7)² + 14 = -84 and -2(+7)² + 14 = -84

x → –7– = (-ve)/(+ve)

=> y → -[infinity].

x → –7+ or x → 7– = (-ve)/(-ve)

=> y → [infinity]

x → 7+ = (-ve)/(+ve)

=> y → -[infinity].

x → 7+, y → –[infinity]. is the correct option

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1