Questions and Answers
What is the result of (fg)(x) where f(x) = 10x - 3 and g(x) = 6x + 8?
-88x³ + 48x² + 88x - 48
What is the result of (fg)(x) where f(x) = 2x - 9 and g(x) = 4x + 5?
8x² - 26x - 45
What is the result of (fg)(x) where f(x) = 5x - 1 and g(x) = 5x + 3?
25x² + 10x - 3
What is the result of (fg)(x) where f(x) = 2x - 3 and g(x) = 4x + 5?
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What is the result of (fg)(x) where f(x) = x - 3 and g(x) = 4x - 2?
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What is the result of (fg)(x) where f(x) = 3x + 7 and g(x) = -2x - 3?
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What is the result of (fg)(x) where f(x) = 5x - 3 and g(x) = x + 1?
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What is the result of (fg)(x) where f(x) = 4x - 7 and g(x) = 9x - 1?
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What is the result of (fg)(x) where f(x) = 6x - 4 and g(x) = x + 6?
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What is the result of (fg)(x) where f(x) = -40b³ + 55b² + 16b - 22?
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Study Notes
Polynomial Expressions
- Polynomials are mathematical expressions involving variables raised to whole number powers.
- Each polynomial is composed of terms that include coefficients, variables, and exponents.
- Degree of a polynomial is determined by the highest power of the variable present.
Examples of Polynomial Forms
- -88x³ + 48x² + 88x - 48: A cubic polynomial with coefficients -88, 48, 88, and -48.
- -35k³ + 70k² + 15k - 30: Another cubic polynomial whose terms reflect similar structures.
- 32m³ - 16m² + 24m - 12: This polynomial has a cubic term, a quadratic term, a linear term, and a constant.
- 20x³ - 18x² - 50x + 45: Features a cubic term that dominates the polynomial, highlighting its non-linear nature.
- -40b³ + 55b² + 16b - 22: A cubic polynomial that illustrates a variety of coefficients.
- 45r³ + 50r² + 63r + 70: Exhibits a positive leading term, indicating growth behavior as r increases.
Function Multiplication
- Functions can be multiplied together to create a new polynomial expression representing their combined behavior.
- Example f(x) = 10x - 3 and g(x) = 6x + 8 leads to (fg)(x) = 60x² + 62x - 24.
- Example f(x) = 2x - 9 and g(x) = 4x + 5 results in (fg)(x) = 8x² - 26x - 45.
Additional Function Combinations
- (fg)(x) for polynomials like f(x) = 5x - 1 and g(x) = 5x + 3 yields 25x² + 10x - 3.
- Combining f(x) = 2x - 3 and g(x) = 4x + 5 gives (fg)(x) = 8x² - 2x - 15, showing interaction between linear terms.
- Each combination reflects how changing coefficients influences the final product.
Evaluating Function Products
- Determining (fg)(x) involves applying distribution across the terms in f(x) and g(x).
- Understanding polynomial multiplication is critical for grasping advanced algebra concepts.
- Each resultant polynomial showcases a unique combination of structural components from the original functions.
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Test your understanding of the multiplication of functions with these flashcards. Each card presents a polynomial expression for you to analyze. Challenge yourself to identify the product of given functions and expand your mathematical skills.