Final answer:
To find the explicit function for a sequence where the output is 'y' and the input is 'x', we analyze each given function option based on the properties of exponents. Without additional information regarding the numeric sequence, we cannot determine which option is correct, but we can describe how each function will behave for a given 'x' value.
Step-by-step explanation:
The student is asking for an explicit function for a sequence, where 'y' is the output and 'x' is the input. Based on the provided information, we can say that raising a number to a power essentially means multiplying that number by itself for the number of times indicated by the exponent. Given this, we can assess each function option provided:
- Option A suggests y(x) = 4(x-1), which means the function value at x will be 4 raised to the power of (x minus 1). This results in a sequence that starts with 1 when x=1, and then increases by a factor of 4 for each subsequent value of x.
- Option B, which is y(x) = 1/4 × 4x, starts with a value of 1 (40 = 1) and also increases by a factor of 4 for each subsequent x, but the initial term is multiplied by 1/4.
- Option C, y(x) = 1/4 × 4(x-1), starts with a value of 1/4 and increases by a factor of 4 for each subsequent x.
- Option D describes a polynomial function, y(x) = x4, which is distinctly different from the exponential nature of the other options.
Using the properties of exponents and the explicit nature of the defined sequence, we can determine which function provides the correct output for each input 'x'. Each option has different implications for the sequence it defines, and the correct option should match the sequence given by the student (which seems to be missing in the prompt).