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A cubic function is a type of polynomial function where the highest degree of the variable (usually represented by x) is 3. The general form of a cubic function is given by: [ f(x) = ax^3 + bx^2 + cx + d n this case, the function is simpler: [ f(x) = 2 x^3 Here’s what you need to know about cubic functions:

• They can have up to three real roots (where the function crosses the x-axis).
• They possess a point of inflection where the curve changes direction. In this example, the point of inflection is at the origin (0,0).
• The shape of a cubic function can vary, but typically, it will have an

The domain and range of a function are essential concepts in understanding how a function behaves. Let's break them down:

Domain: The domain of a function is the set of all possible input values (x-values) that the function can accept. For the cubic function given by 2x^3,

• Since it's a polynomial function, there's no restriction on the x-values.
• This means that the domain is all real numbers, written in interval notation as (-∞, ∞)

Range: The range of a function is the set of all possible output values (y-values) that the function can produce. For our cubic function:

• As x approaches positive infinity, f(x) also approaches positive infinity.
• As x approaches negative infinity, f(x) approaches negative infinity.
• Therefore, the function can produce any y-value, making the range all real numbers, written as (-∞, ∞).

When graphing a function, it's helpful to plot points to understand the general shape of the curve. Follow these steps:

1. **Select x-values:** Choose a range of x-values to compute the corresponding f(x) values. For example, you can select -2, -1, 0, 1, and 2.

2. **Calculate f(x):** Use the function 2x^3 for each x-value:

• For x = -2, f(x) = 2(-2)^3 = -16
• For x = -1, f(x) = 2(-1)^3 = -2
• For x = 0, f(x) = 2(0)^3 = 0
• For x = 1, f(x) = 2(1)^3 = 2
• For x = 2, f(x) = 2(2)^3 = 16

3. **Plot points:** Plot each (x, f(x)) pair on a coordinate grid: - (-2, -16) - (-1, -2) - (0, 0) - (1, 2) - (2, 16)

4. **Draw the curve:** Connect the plotted points smoothly to reflect the continuous nature of the polynomial. Remember, the curve should smoothly pass through these points. This process will give you a clear visual understanding of how the function behaves. It's crucial to choose a range of x-values that show the important features of the function's graph, particularly where it changes direction.