Final answer:
The highest power of x in the function f(x)=0.02(x−1)3(x²)2(x³)(x−3) is 3 after simplifying the terms, indicating that the graph of the function is a cubic graph, so the correct answer is A. Cubic graph.
Step-by-step explanation:
To determine the type of graph represented by the function f(x)=0.02(x−1)3(x²)2(x³)(x−3), we need to analyze the highest power of the variable x in the equation. The given function can be simplified by multiplying the powers of x. We have:
- x-1 which is x to the power of -1
- x22 which simplifies to x to the power of 4 (since 2 times 2 equals 4)
- x3 which is x to the power of 3
- x-3 which is x to the power of -3
Now, adding all the exponents (with consideration for their signs), we get: -1 + 4 + 3 - 3 = 3. This means the highest power of x in the function is 3, which indicates that the graph of the given function would be a cubic graph. Therefore, the correct answer is A. Cubic graph.