find all vertical asymptotes of the following function.\n f(x)=\frac{2 x^{2}-7 x}{2 x^{2}+8 x-10} \nanswer…
find all vertical asymptotes of the following function.\n f(x)=\frac{2 x^{2}-7 x}{2 x^{2}+8 x-10} \nanswer attempt 1 out of 2\nno vertical asymptotes
Answer
Explanation:
Step1: Factor numerator and denominator
Numerator: (2x^{2}-7x = x(2x - 7)) Denominator: (2x^{2}+8x - 10=2(x^{2}+4x - 5)=2(x + 5)(x - 1)) So (f(x)=\frac{x(2x - 7)}{2(x + 5)(x - 1)})
Step2: Find values that make denominator zero
Set (2(x + 5)(x - 1)=0) (x+5 = 0) gives (x=-5) (x - 1=0) gives (x = 1)
Step3: Check if these values make numerator zero
For (x=-5): (2(-5)^{2}-7(-5)=50 + 35=85\neq0) For (x = 1): (2(1)^{2}-7(1)=2 - 7=-5\neq0)
Answer:
The vertical asymptotes are (x=-5) and (x = 1)