Question

The graph below shows three functions. Which function has all real numbers as its domain

A. Only f(x)

B. Both g(x) and p(x)

C. Both f(x) and g(x)

D. Only p(x)

Answer 1

C. Both f(x) and g(x)

Explanation:

We are given,

Graphs of three function namely f(x), g(x) and p(x).

It is require to find the functions having the set of real numbers as the domain.

From the graph, we have,

The domain of the function p(x) is a subset of [-2,2] and is not the set of all real numbers.

Whereas, the domain of the functions f(x) and g(x) is the set of all real numbers.

Hence, option C is correct.

Answer 2

Option C is correct.

Step-by-step explanation:

Domain is the values of x for f function

Here, we have g(x) and f(x) which are extending on x-axis and is not terminated anywhere

Hence, their domain is the real number

Therefor, Option C is correct.

Option A is discarded because not only f(x) but g(x) also has real numbers as domain

Option B and D are discarded because p(x) does not have all real numbers as domain.