Final answer:
The question is about finding integer coordinate points on the function f(x)=3(1/3)^x. The task involves calculating the function's output values for integer x values to see if they also yield integer y coordinates. Key concepts include exponentiation and the behavior of exponential functions.
Step-by-step explanation:
The student is asking about finding points with integer coordinates on the graph of a function, specifically f(x)=3(1/3)^x, where x is an integer. In mathematics, this involves determining the output values of the function that result in integer coordinates when the input (x) is limited to integer values. To do this for the given function, we plug in integer values for x and find the corresponding y values that are integers.
For example, when x = 0, f(0) = 3(1/3)^0 = 3(1) = 3, which is an integer. The same process can be applied for other integers, keeping in mind that for negative integers, the exponents will create fractions due to the 1/3 base. Therefore, one must be careful only to select values of x that result in y also being an integer.
Cubing of exponentials involves cubing the constant term and multiplying the exponent by 3. The rule for exponentiation, such as in 3^2.35, is to add exponents when multiplying like bases: x^p * x^q = x^(p+q). This rule can help in simplifying expressions with exponential terms.