Show all work to identify the asymptotes and zero of the function f of x equals 5 x over quantity x squared minus 25

Using function concepts, it is found that:

The function is given by:

Applying the subtraction of perfect squares, the function will be given by:

The zero is the value of x for which:

In a fraction, it is when the numerator is zero, thus:

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, thus:

The horizontal asymptote is:

Hence:

A similar problem is given at link

VA: x = {-5, 5), HA: y = 0, Zeros: x = 0

Step-by-step explanation:

Vertical asymptotes: The denominator cannot equal zero.

x² - 25 = 0  

(x - 5)(x + 5) = 0

x = 5, x = -5

Horizontal Asymptote: Let m represent degree of numerator and n represent the degree of the denominator.

For the given equation, m = 1 and n = 2 so we use option 3 --> y = 0

Zeros: Set the equation equal to zero and solve for x.

Multiply both sides by x²- 25   -->    0 = 5x

Divide both sides by 5       -->          0 = x

the 3rd on is correct

step-by-step explanation: