Algebra 2 VA SOL Review Flashcards

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.