Question

which of the following functions are continuous for all real numbers?
h(x) = sin(x)
f(x) = cos(x)
choose 1 answer:
a h only
b f only
c both h and f
d neither h nor f

Explanation:

The sine function \( h(x)=\sin(x) \) and the cosine function \( f(x)=\cos(x) \) are both continuous for all real numbers. The domain of \( \sin(x) \) and \( \cos(x) \) is all real numbers, and their graphs are smooth, unbroken curves with no holes, jumps, or asymptotes over the entire real - number line. So both \( h(x) \) and \( f(x) \) are continuous for all real numbers.

Answer:

C. Both \( h \) and \( f \)