Questions and Answers
What is a polynomial equation?
An equation in which the coefficients are real numbers and the exponents are whole numbers.
What is an inverse function?
A function that maps output back to input.
What are radical equations?
Equations that contain radical symbols or rational exponents.
How are a function and its inverse related?
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What is the DOS formula?
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What is the DOC formula?
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What is the SOC formula?
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How does one know if a variable is a square?
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How does one know if a variable is a cube?
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What does the highest exponent tell one when solving a polynomial equation?
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How does one find an inverse function?
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What is the notation for an inverse function?
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What three things do a function and its inverse have?
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What must one do when solving radical equations at the last step?
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When do you put the plus/minus sign when solving radical equations?
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Study Notes
Polynomial Equation
- Defined as an equation with real number coefficients and whole number exponents.
Inverse Function
- A function that reverses the mapping of a given function, taking outputs back to their original inputs.
Radical Equations
- Equations that include radical symbols such as square roots, or have rational exponents.
Relationship between Function and Inverse
- Functions and their inverses are symmetrical around the line y=x; they essentially reflect over this line.
DOS Formula
- Represents the difference of squares: (a + b)(a - b), where "a" and "b" are square roots.
DOC Formula
- Represents the difference of cubes: (a - b)(a² + ab + b²), where "a" and "b" are cube roots.
SOC Formula
- Represents the sum of cubes: (a + b)(a² - ab + b²), where "a" and "b" are cube roots.
Identifying Square Variables
- A variable is identified as a square if its exponent is divisible by 2; finding it involves dividing the exponent by 2.
Identifying Cube Variables
- A variable qualifies as a cube if its exponent is divisible by 3; to determine it, divide the exponent by 3.
Highest Exponent in Polynomial Equations
- Indicates the maximum number of potential solutions for the equation based on its degree.
Finding an Inverse Function
- Achieved by swapping the x and y values in the original function.
Notation for Inverse Function
- Denoted as f⁻¹(x), interpreted as "F's inverse of x" or "F to the negative first power".
Characteristics of Functions and Their Inverses
- Share reciprocal slopes, meet at points where x and y values are equal, and reflect over the line y=x.
Final Step in Solving Radical Equations
- Requires checking for extraneous solutions to ensure correctness.
Plus/Minus Sign in Radical Equations
- Introduced in solutions when the index of the radical is even, indicating two possible solutions.
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Description
Test your knowledge on key terms and concepts in Algebra 1, specifically focusing on Unit 7. This set of flashcards covers polynomial equations, inverse functions, and radical equations. Perfect for quick revisions or preparation for exams.
