Question

What is the base for this equation, and what type of function is it?

[g(x) = 3((1)(4))ˣ⁻² - 3]
A. Base: ((1)(4)), Exponential function
B. Base: 3, Exponential function
C. Base: 4, Logarithmic function
D. Base: 2, Linear function

Answer 1

The correct base for the given equation g(x) = 3(1×4)^(x-2) - 3 is 4, and the function is an exponential function. The answer is therefore A: Base: 4, Exponential function.

The correct answer is A.

Step-by-step explanation:

The equation given is g(x) = 3(1×4)x-2 - 3. This is an exponential function because it has the form f(x) = abx, where 'a' and 'b' are constants, and 'b' is the base raised to the 'x' power, which is a variable exponent. The (1×4) in the equation simplifies to 4, so the base is really just 4. Additionally, the expression has been modified by a translation (subtracting 3), which affects the graph but not the nature of the function as exponential.

Option B, which suggests the base is 3, is incorrect because 3 is the coefficient that multiples the entire exponential expression, not the base of the exponent. Furthermore, Options C and D are incorrect as C suggests it's a logarithmic function, which would require the dependent variable to be inside a log expression, not an exponent. Option D suggests a linear function, which is not represented by having an exponent on the variable.

Hence, the correct answer is A: Base: 4, Exponential function.