# Which statements accurately describe the function f(x) = 3? check all that apply.

Asked by wiki @ in Mathematics viewed by 289 People

Which statements accurately describe the function f(x) = 3√18^x? Check all that apply.

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 √2.
F. The simplified base is 3√2.

The correct options are:

A) The domain is all real numbers;
C) The initial value is 3; and
F) The simplified base is 3√2.

Explanation:

A) The domain is the set of numbers that can be use for x. In this function, there are no domain restrictions; this means there are no values for x that will not give you a value for y. This means that all numbers work, which we say is "the set of all real numbers."

C) To find the initial value (starting point), substitute 0 for x:
f(x) = 3(√18)ˣ
f(0) = 3(√18)⁰
f(0) = 3(1) = 3

Thus the initial value is 3.

F) The base of the current function is √18; this is because that is what is raised to a power. If we simplify this, we find the prime factorization of 18, looking for pairs of factors to take out.

The prime factorization of 18:
18 = 2*9
9 = 3*3

This means 18 = 2*3*3; it gives us √18 = √(2*3*3). We have a pair of 3's under the radical, so we take a 3 out; this leaves a 2 under the radical:
√18 = √(2*3*3) = 3√2.

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