Question

What is the graph of f(x)=0.02(x−¹)3(x ²)2(x ³)(x−³)?

A. Cubic graph
B. Quartic graph
C. Quintic graph
D. Sextic graph

Answer 1

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.