Give the equations of any vertical asymptotes for the graphs of the rational functions.
f(x)=(3x³+6x-6)/(x²+3x-10)
for vertical asymptotes, the denominator becomes zero
so x^2 + 3x - 10 = 0
(x+5)(x-2) = 0
x = -5 or x - 2 are vertical asymptotes.
To find the equations of vertical asymptotes for a rational function like f(x) = (3x³+6x-6)/(x²+3x-10), we need to look for values of x that make the denominator of the function equal to zero.
In this case, the denominator of the function is x²+3x-10.
To find the values of x that make the denominator zero, we need to solve the quadratic equation x²+3x-10 = 0.
We can factor this quadratic equation or use the quadratic formula to solve for x.
Factorizing the equation gives us: (x+5)(x-2) = 0.
Setting each factor equal to zero, we get two possible values for x: x+5 = 0 or x-2 = 0.
Solving these equations, we find x = -5 or x = 2.
These are the values of x that make the denominator zero and will result in vertical asymptotes for the graph of the rational function.
Therefore, the equations of the vertical asymptotes for the graph of f(x) = (3x³+6x-6)/(x²+3x-10) are x = -5 and x = 2.