Question

Which statements accurately describe the function f(x) =3(18)? Select three options.

a.The domain is all real numbers.
b. The range is y ; 3.
c.The initial value is 3.
d.The initial value is 9.
e.The simplified base is 3/2.

Answer 1

The function f(x) = 3(18) is a constant function where the domain is all real numbers, the range is a single value y = 54, and the 'initial value' is 54, since the variable x is not present in the equation.

Step-by-step explanation:

The function in question, f(x) = 3(18), appears to be lacking the variable x in its expression and thus represents a constant function. When analyzing such a function, it's essential to realize that the value will always be the result of the single multiplication of 3 and 18, which is 54. Therefore, the following attributes can be deduced:

• The domain of this function is all real numbers, as there's no value of x that will not work in this function since x is not present.
• The range is a single value, y = 54, since no matter what x value you choose, the outcome of the function will always be 54.
• The initial value is often considered the value of the function when x equals 0, which in this case is still 54, making the term 'initial value' a bit of a misnomer, as there's no actual computation involving x.

Based on these details:

1. Answer (a) 'The domain is all real numbers.' is correct.
2. Answer (b) 'The range is y = 54.' would be accurate if it was phrased in this way, not 'The range is y = 3' as stated.
3. Answer (c) 'The initial value is 3.' is incorrect, as the initial value of this function is 54, not 3.
4. Answer (d) 'The initial value is 9.' also does not describe this function appropriately.
5. Answer (e) 'The simplified base is 3/2.' is not relevant as this function does not involve an exponential form or a simplified base.