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Questions and Answers
What is the inverse of f(x)?
What is the inverse of f(x)?
Switch x and y
What do you need to do to solve a problem involving normally distributed data with a mean and standard deviation?
What do you need to do to solve a problem involving normally distributed data with a mean and standard deviation?
Draw the curve and label the bottom, using the 68, 95, 99.7 rule.
How do you factor 8x^3 + 27?
How do you factor 8x^3 + 27?
(2x + 3)(4x^2 - 6x + 9)
What do the terms roots, zeros, and solutions refer to?
What do the terms roots, zeros, and solutions refer to?
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Can you crush this test?
Can you crush this test?
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What is the equation when Y varies proportionally with another variable?
What is the equation when Y varies proportionally with another variable?
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Where should you look on the graph for the end behavior of f(x) as x approaches negative infinity?
Where should you look on the graph for the end behavior of f(x) as x approaches negative infinity?
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Where should you look on the graph for the end behavior of f(x) as x approaches infinity?
Where should you look on the graph for the end behavior of f(x) as x approaches infinity?
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What does 'find the solution set' mean?
What does 'find the solution set' mean?
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What does the notation { } mean?
What does the notation { } mean?
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What should you do if you have no idea how to start a problem?
What should you do if you have no idea how to start a problem?
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What should you do if you seriously have no clue what to do?
What should you do if you seriously have no clue what to do?
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Should you ever zone out during an S.O.L?
Should you ever zone out during an S.O.L?
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What does 'domain' refer to?
What does 'domain' refer to?
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What does 'range' refer to?
What does 'range' refer to?
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What is a horizontal asymptote?
What is a horizontal asymptote?
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What is a vertical asymptote?
What is a vertical asymptote?
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What do you do if you see f(g(2))?
What do you do if you see f(g(2))?
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What should you look for when finding the solution set for a system of equations on a graph?
What should you look for when finding the solution set for a system of equations on a graph?
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How do you find the best model for a table of numbers?
How do you find the best model for a table of numbers?
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What is the constant of proportionality?
What is the constant of proportionality?
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Study Notes
Inverse Functions
- The inverse of f(x) is found by switching x and y coordinates.
Probability and Normal Distribution
- For normally distributed problems, draw a curve and label the x-axis.
- Place the mean in the center, add and subtract standard deviations three times for intervals.
- Apply the 68-95-99.7 rule to evaluate probability ranges.
Factoring Techniques
- Factor the polynomial 8x^3 + 27 using SOAP (Sum of Cubes).
- The factorization results in (2x + 3)(4x² - 6x + 9).
Understanding Roots and Zeros
- Roots, zeros, and solutions refer to x-intercepts where f(x) = 0.
- For systems of equations, identify intersection points (x, y) instead.
Confidence in Testing
- Maintain a positive attitude; preparation is key for success.
Direct Variation
- When “Y varies proportionally with...” appears, use the equation y = k.
- Inverse relationships place the constant on the bottom; jointly varies involves multiplication.
Analyzing End Behavior
- For end behavior as x approaches negative infinity, observe the left end of the graph.
- The graph's upward trend indicates f(x) approaches infinity, downward indicates negative infinity.
Analyzing End Behavior (Continued)
- For end behavior as x approaches infinity, look at the right end of the graph.
- Similar trends apply for upward or downward movement of f(x).
Solution Set Interpretation
- "Find the solution set" means to solve the equation, which may yield multiple or no solutions.
Recognition of No Solution
- The symbol { } signifies that no solution is an option; verify results by substituting back into the original equation.
Strategies for Unknown Problems
- If unsure how to start, read the problem thoroughly, identify familiar terms, and consult the formula sheet.
Dealing with Tough Problems
- If completely lost, skip the problem; focus on questions that are manageable.
Staying Engaged During Tests
- It’s acceptable to zone out briefly during an S.O.L.; regroup and continue with concentration.
Domain and Range
- Domain refers to the input values of a function (left to right).
- Range refers to the output values (down to top).
Asymptotes
- Horizontal asymptotes are expressed as y = constant; they determine the function’s behavior at extremes.
- Vertical asymptotes are expressed as x = constant; they show restrictions in the domain of the function.
Function Composition
- To evaluate f(g(2)), first substitute 2 into g, then take that result to evaluate f.
Solving Systems of Equations Graphically
- Look for the intersection points of two lines on the graph to find the solution set.
Modeling Data
- To find the best model for a set of numerical data, utilize a calculator.
- Enter the data under STAT → Edit, then use STAT → Calc to assess regression options based on the highest r² value.
Constant of Proportionality
- In problems involving variation, K represents the constant of proportionality in the equation y = kx.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Review key concepts in Algebra 2 with these flashcards, perfect for the Virginia Standards of Learning. Each card covers critical topics such as inverse functions, normal distribution, and factoring polynomials to help reinforce your understanding. Ideal for exam preparation and self-assessment.
