Question

The function f is an increasing function such that every time the output values of the function f increase by 1, the corresponding input values multiply by 4. Which of the following could define f(x)?

A.) x^4
B.) 4^x
C.)4 square root of x
D.) log4x

Answer 1

The function that increases its output by 1 when its input is multiplied by 4 can be defined by the logarithmic function f(x) = log4(x), which fits the given condition. Therefore correct option is D

Step-by-step explanation:

The function that is described as increasing such that every time the output values increase by 1, the corresponding input values multiply by 4, can be represented by a logarithmic function with base 4. This is because the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.

Therefore, the function f(x) = log4(x) fits the description given. As the input value is multiplied by 4, which is the base of the logarithm, the output value increases by 1, as logarithms convert multiplication into addition.

Answer 2

The function that matches the description where the output increases by 1 and the corresponding input value multiplies by 4 is D) log4(x), which is a logarithmic function with a base of 4.

Step-by-step explanation:

The question asks which function would correspond to an increasing function where the output increases by 1 and the corresponding input multiplies by 4. This is characteristic of exponential functions, specifically a logarithmic function with a base of 4. So, when the output of f(x) increases by 1, the input x would have been raised to the next power of 4.

The correct choice that matches this description is D) log4(x). This is because the logarithm of a number with a particular base tells us the power to which the base must be raised to produce that number. Hence, for every unit increase in the logarithmic function, the corresponding input value is multiplied by the base, which in this case is 4.