Question

Show all work to identify the asymptotes and state the end behavior of the function f of x is equal to 4x divided by the quantity of x minus 16 end quantity.

Answer 1

Explanation:

The function f(x) = 4x/(x-16) has two vertical asymptotes at x = 16. This can be seen by taking the limit of the function as x approaches 16 from the left and right sides.

On the left side, as x approaches 16 from the left, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach -∞. This results in a limit of -∞, indicating a vertical asymptote at x = 16.

On the right side, as x approaches 16 from the right, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach +∞. This results in a limit of +∞, also indicating a vertical asymptote at x = 16.

The end behavior of the function is that as x approaches +∞, the function will approach +∞, and as x approaches -∞, the function will approach -∞.