Questions and Answers
When we compose functions, we must make sure that the output of the first function is part of the ___ of the second function.
In general, the composition of functions is not ___.
We expect to see a ___ for the graph of a composition of a function and its inverse function, if the domain of each is all real numbers.
Find the composition of the function.
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Find the composition of the function.
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Find the composition of the function.
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Find the composition of the function.
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Find the composition of the function.
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Find the composition of the function.
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Find the composition of the function.
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Find the composition of the function.
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Find the composition of the function.
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Find the composition of the function.
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Find the equation of the circle with center (-2, 5) and radius 5.
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Find the product (x + 3)^3.
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Study Notes
Function Composition
- Ensure the output of the first function is included in the domain of the second function for proper composition.
- The composition of functions is generally not commutative, meaning the order of functions matters.
Graphs and Inverses
- A graph representing the composition of a function and its inverse, when both have domains as all real numbers, should ideally form a line.
Composition Examples
- Compositions can yield outputs such as:
- x^(1/6) for certain functions.
- x^(-1/2) reflecting exponentiation rules.
- x^6 illustrating polynomial growth.
Rational Functions
- Compositions may produce forms like 1/(x+5), demonstrating how functions interact through division.
Linear Functions
- Finding compositions can lead to linear transformations, such as results of x-3 or adjusting constants in expressions like x-6.
Circle Equation
- The equation for a circle centered at (-2, 5) with a radius of 5 follows the standard form:
- (x+2)² + (y-5)² = 25.
Polynomial Expansion
- Expanding functions results in expressions such as the product of (x+3)³, yielding:
- x³ + 9x² + 27x + 27, showcasing the binomial expansion.
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Description
Test your understanding of function composition with this set of flashcards designed for Algebra 2, Unit 7, Lesson 9. Each card presents a question about key concepts that are crucial for understanding function operations. Perfect for study and review before exams!
