Algebra 2 Test 6 Review Flashcards

Simplifying Expressions

• To simplify 7 - 2 * 5 + 9 + 3, apply order of operations: 7 - 10 + 9 + 3 = 0.

Objective Function

• For Mrs. Drake selling skirts and dresses, the profit function is P = 5x + 12y, where x represents skirts and y represents dresses.

Domain of Functions

• The domain of the function ƒ(x) = (s - 5) / (x + 6) excludes x = -6, giving the domain: (-∞, -6) and (-6, ∞).

Distance Between Points

• The distance between points (-2, 2) and (1, 6) calculates to 5, using the distance formula.

Standard Form of Complex Numbers

• The standard form for complex numbers is represented as a + bi; 7 - 4i fits this definition.

Inverse Relationships

• Given y = 3 when x = 4, y can be determined when x = 6. The result is y = 2.

Midpoint Calculation

• The midpoint between points (-2, 2) and (1, 6) is (-1, 4), calculated by averaging the x and y coordinates.

Matrix Dimensions

• Multiplying a 2x4 matrix by a 4x2 matrix results in a 2x2 matrix.

Transformations of Functions

• The transformation of the parabola represented by ƒ(x) = x² - 6 is a vertical translation.

Matrix Identification

• The matrix [¹₀ ⁰₁] is identified as an identity matrix.

Solving Equations

• The equation x⁴ - 2x² - 3 = 0 yields solutions x = ±i and x = ±√3.
• For x² - 6x = 5, solutions are x = 3 ± √14.
• The cubic equation x³ - 3x² - 4x + 12 = 0 has solutions x = 2, -2, 3.

Absolute Value Inequalities

• The solution to |2x - 3| - 5 ≤ 8 includes all values in the interval [-5,8].

Graphing Solutions

• The inequality x² + 4x - 12 ≥ 0 yields solutions in intervals (-∞, -6] and [2, ∞).

Function Operations

• For functions f(x) = x² + 2x and g(x) = x - 3, the product (fg)(x) results in x³ - x² - 6x.
• The composition (f ⁰ g)(x) yields x² - 4x + 3.

Graphing Parabolas

• The graph of f(x) = (x - 2)² + 3 has its vertex at (2, 3), with significant points at (4, 12) and (5, -7).

Inequalities

• Graphing the solution for the inequality 2x - 3y requires further specification for x and y ranges.