Practice Definition Of A Cubic Function (1) - Cubic Functions - IB 10 Mathematics

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6 sample questions

Question 1.
Write the general form of a cubic function.
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What powers of x are present?
Question 2.
What is the maximum number of real roots a cubic function can have?
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Consider how a graph can intersect the x-axis.
3Question 3.
What is the general form of a cubic function?
- f(x) = ax² + bx + c
- f(x) = ax³ + bx² + cx + d
- f(x) = ax⁴ + bx³ + cx² + d
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Remember the degree of the polynomial.
4Question 4.
True or False: A cubic function can have four real roots.
- True
- False
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Think about the highest degree of the polynomial.
Question 5.
Given the cubic function f(x) = 2x³ - 6x² + 4x - 8, find the roots using the Rational Root Theorem.
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Check divisors of the constant term against those of the leading coefficient.
Question 6.
Sketch the graph of a cubic function with known roots x = -1, x = 2, and x = 3, considering the multiplicity of roots.
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Remember the end behavior: observe the leading coefficient to determine how the curve behaves as it approaches ±∞.

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