Let f(x= -3
________________
(x+2) (2x-5)
Specify any zeros, and asymptotes of
f(x).
To find the zeros and asymptotes of the function f(x), we need to determine the values of x that make the numerator of the fraction equal to zero and identify any vertical asymptotes.
First, let's find the zeros by setting the numerator of the fraction equal to zero:
-3 = 0
Since -3 is a constant value, it is not possible for it to equal zero. Therefore, the equation has no zeros.
Next, let's identify the vertical asymptotes. For a rational function, vertical asymptotes occur when the denominator of the fraction equals zero:
(x + 2)(2x - 5) = 0
To find the values of x that make the denominator equal to zero, we solve the equation:
x + 2 = 0 or 2x - 5 = 0
Solving these equations gives us:
x = -2 and x = 5/2 = 2.5
Therefore, the vertical asymptotes of f(x) are x = -2 and x = 2.5.
In summary, the function f(x) has no zeros and has two vertical asymptotes: x = -2 and x = 2.5.