y=2x^2+3/x-1
how would you find the x intercept and vertical asymptote?
To find the x-intercept and vertical asymptote of the given function y = (2x^2 + 3) / (x - 1), we need to set the numerator equal to zero to find the x-intercepts and determine the value of the denominator to find the vertical asymptote.
1. X-intercept:
To find the x-intercept, we set the numerator of the function, 2x^2 + 3, equal to zero and solve for x.
2x^2 + 3 = 0
Now, we can solve this quadratic equation for x by factoring or using the quadratic formula.
Factoring method:
2x^2 + 3 = 0
(2x + 1)(x + 3) = 0
Setting each factor equal to zero:
2x + 1 = 0
x = -1/2
x + 3 = 0
x = -3
Therefore, the x-intercepts are at x = -1/2 and x = -3.
2. Vertical asymptote:
To find the vertical asymptote, we need to determine the value of the denominator, x - 1, where the function approaches infinity or negative infinity.
Setting the denominator equal to zero:
x - 1 = 0
x = 1
So, the vertical asymptote is at x = 1.
In summary:
- The x-intercepts of the function are at x = -1/2 and x = -3.
- The vertical asymptote of the function is at x = 1.