Hich statements about the function f are true? Check all that apply. The domain of f(x) is {all real numbers}. The range of f(x) is {all real numbers}. The domain of f(x) is {x| x > 0}. The range of f(x) is {y| y > 0}. f(2) = 4 f(2) = 2(x + 3)

A. The domain of f(x) is {all real numbers}.

B. The range of f(x) is {all real numbers}

E. f(2) = 4

Explanation

Find the graph attached.

The domain of a function is the value of the input variable x for which the function f(x) exists. Given the function

f(x) = 1/2 x + 3

The function will exist on all values of x (either positive or negative).

The domain can be said to exist on all real values. If you look at the graph, we will see that the line tends to both negative infinity and positive infinity. Hence the domain can be represented according to the set notation:

DOMAIN: (-∞, ∞)

The range is the set of output value y for all input variable x. The output value y will also exist on all real values because, no matter the value of x imputed in the function, we will always get a finite value as the output. Hence the range of the function is denoted by the set notation:

RANGE:  (-∞, ∞)

Next is to get f(2).

To get f(2), we will set the input value as 2 and calculate for the output value as shown:

f(2) = 1/2(2) + 3

f(2) = 1+3

f(2) = 4

Hence the following are true of the function:

The domain of f(x) is {all real numbers}.

- The range of f(x) is {all real numbers}

- f(2) = 4