given the function, f(x) = -4 / (2x²+0x - 56)...
given the function, f(x) = -4 / (2x²+0x - 56) what are the vertical asymptotes? x = 7, x = -4 x = 0 x = -7, x = 4 there is no vertical asymptote.
Answer
# Explanation:
## Step1: Find the denominator's roots
Set the denominator $2x^{2}+6x - 56=0$. First, factor out the greatest - common factor. Factor out 2: $2(x^{2}+3x - 28)=0$. Then factor the quadratic inside the parentheses: $x^{2}+3x - 28=(x + 7)(x - 4)=0$.
## Step2: Solve for x
Using the zero - product property, if $(x + 7)(x - 4)=0$, then $x+7 = 0$ or $x - 4=0$. Solving $x+7 = 0$ gives $x=-7$, and solving $x - 4=0$ gives $x = 4$. For a rational function $y=\frac{f(x)}{g(x)}$, vertical asymptotes occur at the values of $x$ that make the denominator $g(x)=0$ and the numerator $f(x)\neq0$. Here, the numerator is $-4\neq0$. So the vertical asymptotes are $x=-7$ and $x = 4$.
# Answer:
C. $x=-7,x = 4$