Questions and Answers
What is a rational number?
What is an irrational number?
What are functions?
Each input is paired to exactly one output.
What is the zero of a function?
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What does 'domain' refer to in mathematics?
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What does 'range' refer to in mathematics?
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What is the vertical line test used for?
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Linear equations have multiple outputs for the same input.
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What is the slope-intercept form of a line?
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What is the standard form of a linear equation?
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What is the point-slope form of a linear equation?
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What are parallel lines?
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What are perpendicular lines?
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What is direct variation?
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What happens when solving an inequality and you multiply or divide by a negative number?
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How do you graph a linear inequality?
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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).
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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.
