find all vertical asymptotes of the following function.\n\n f(x)=\frac{2 x^{2}+7 x}{3 x^{2}+3 x - 90}…

find all vertical asymptotes of the following function.\n\n f(x)=\frac{2 x^{2}+7 x}{3 x^{2}+3 x - 90} \n\nanswer attempt 1 out of 2\n\nno vertical asymptotes

find all vertical asymptotes of the following function.\n\n f(x)=\frac{2 x^{2}+7 x}{3 x^{2}+3 x - 90} \n\nanswer attempt 1 out of 2\n\nno vertical asymptotes

Answer

Explanation:

Step1: Factor numerator and denominator

Numerator: (2x^{2}+7x = x(2x + 7)) Denominator: (3x^{2}+3x - 90=3(x^{2}+x - 30)=3(x + 6)(x - 5)) So (f(x)=\frac{x(2x + 7)}{3(x + 6)(x - 5)})

Step2: Find values that make denominator zero

Set (3(x + 6)(x - 5)=0) (x+6 = 0) gives (x=-6); (x - 5=0) gives (x = 5)

Step3: Check if numerator is zero at these values

When (x=-6), numerator (=(-6)(2\times(-6)+7)=(-6)(-12 + 7)=(-6)\times(-5)=30\neq0) When (x = 5), numerator (=5(2\times5+7)=5(10 + 7)=5\times17 = 85\neq0)

Answer:

The vertical asymptotes are (x=-6) and (x = 5)