Algebra Class: Rational Numbers and Functions

Study Notes

Rational and Irrational Numbers

Rational Number: Can be expressed as a fraction, including proper/improper fractions, mixed numbers, and repeating decimals.
Irrational Number: Cannot be expressed as a fraction.

Functions

Functions: Each input (x value) corresponds to exactly one output (y value), ensuring no repeated output values.
Zero of a Function: The x-intercept where the function equals zero (f(x) = 0).

Domain and Range

Domain: Set of all possible input values (x-values) for a function.
Range: Set of all possible output values (y-values) for a function.

Vertical Line Test

Vertical Line Test: A method to determine if a graphed relation is a function; if a vertical line intersects the graph only once, it's a function.

Linear Equations

Slope-Intercept Form: Written as ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.
Standard Form: Expressed as ( Ax + By = C ) where A, B, and C are integers.
Point-Slope Form: Written as ( y - y_1 = m(x - x_1) ), where ( m ) is the slope and ( (x_1, y_1) ) is a point on the line.

Lines and Their Relationships

Parallel Lines: Two lines that have identical slopes, indicating they run alongside each other without intersection.
Perpendicular Lines: Two lines that intersect at right angles, characterized by opposite reciprocal slopes (e.g., slopes of 3 and -1/3).

Direct Variation

Direct Variation: Expressed as ( y = kx ) where ( k ) is the constant of variation (slope). The graph is a straight line passing through the origin.

Inequalities

Solving Inequalities: If multiplying or dividing both sides of an inequality by a negative number, reverse the inequality sign.
Graphing a Linear Inequality: Represented with boundary lines: solid lines for ≤ or ≥ (inclusive) and dotted lines for < or > (exclusive).

Description

Test your understanding of rational and irrational numbers, functions, and linear equations in this engaging algebra quiz. Explore concepts like the slope-intercept form, domain and range, and the vertical line test to elevate your math skills.