Which one or ones of the following statements is/are true?

if the line x = 1 is a vertical asymptote of y = f(x), then f is not defined at x = 1.
if f(2) > 0 and f(4) < 0, then there exists a number c between 2 and 4 such that f(c) = 0.
if f is continuous at x = 5 and f(5) = 2 and f(4) = 3, then the limit as x approaches 2 of the quantity 4 times x squared minus 11 equals 2.
a. i only

b. ii only

c. iii only

d. all statements are true.

answer-

solution-

the given function,

the parent cosine function is,

1. for

as there is a negative sign in the cos x, so all the points with coordinate (x, cos x) becomes (x, -cos x)

∴ it is reflected over x-axis.

2. for

as a scale factor of 0.1 (i.e < 1) is multiplied, so it is compressed by a factor of 0.1

3. for

as 4 is subtracted from the f(x), so all point with coordinate (x, f(x)) becomes (x, f(x)-4)

∴ it is translated 4 units down.

therefore, a series of processes

yield the given function from its parent function.