Answer:
To complete the missing parts of the table for the function y = (1/4)^x, we need to substitute different values of x into the equation and calculate the corresponding values of y.
Let's start with x = 0. When x = 0, (1/4)^0 equals 1, because any number raised to the power of 0 is always 1. Therefore, when x = 0, y = 1.
Next, let's consider x = 1. When x = 1, (1/4)^1 equals 1/4, because any number raised to the power of 1 is the number itself. So when x = 1, y = 1/4.
Now, let's move on to x = 2. When x = 2, (1/4)^2 equals 1/16, because we multiply 1/4 by itself. Therefore, when x = 2, y = 1/16.
Continuing with x = 3, (1/4)^3 equals 1/64, because we multiply 1/4 by itself twice. Hence, when x = 3, y = 1/64.
We can follow the same pattern to calculate the values of y for other values of x. For example, when x = -1, (1/4)^(-1) is equal to 4, as we invert the base and the exponent. So when x = -1, y = 4.
To summarize, the completed table for the function y = (1/4)^x would look like this:
x | y
------------
0 | 1
1 | 1/4
2 | 1/16
3 | 1/64
-1 | 4
Remember, when working with exponential functions, the base value (1/4 in this case) determines the rate at which the function decreases or increases as the exponent (x) changes. In this function, as x increases, y decreases exponentially. Conversely, as x decreases, y increases exponentially.
Explanation:
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