Question

Consider function f. Complete the statements describing the discontinuities of function f. Function f has a vertical asymptote at x=___. Function f has a hole at x=___. The end behavior of function f is describe by asymptote___.

a) -2, x=3, y=4
b) 3, x=-2, y=4
c) [infinity], x=3, y= -[infinity]
d) 3, x=[infinity], y=-[infinity]

Answer 1

Function f has a vertical asymptote at x=3, a hole at x=-2, and the end behavior is described by the asymptote y=4.

Step-by-step explanation:

Function f has a vertical asymptote at x=3. This means that as x approaches 3 from either side, the function approaches positive or negative infinity.

Function f has a hole at x=-2. This means that at x=-2, the function is undefined but can be filled by a single point.

The end behavior of function f is described by the asymptote y=4. This means that as x approaches positive or negative infinity, the function approaches y=4.