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Questions and Answers
What is a rational number?
What is a rational number?
- A whole number
- A number that cannot be written as a fraction
- An integer
- A number that can be written as a fraction (correct)
What is an irrational number?
What is an irrational number?
- A number that can be expressed as a fraction
- A negative number
- Any number that cannot be written as a fraction (correct)
- A repeating decimal
What are functions?
What are functions?
Each input is paired to exactly one output.
What is the zero of a function?
What is the zero of a function?
What does 'domain' refer to in mathematics?
What does 'domain' refer to in mathematics?
What does 'range' refer to in mathematics?
What does 'range' refer to in mathematics?
What is the vertical line test used for?
What is the vertical line test used for?
Linear equations have multiple outputs for the same input.
Linear equations have multiple outputs for the same input.
What is the slope-intercept form of a line?
What is the slope-intercept form of a line?
What is the standard form of a linear equation?
What is the standard form of a linear equation?
What is the point-slope form of a linear equation?
What is the point-slope form of a linear equation?
What are parallel lines?
What are parallel lines?
What are perpendicular lines?
What are perpendicular lines?
What is direct variation?
What is direct variation?
What happens when solving an inequality and you multiply or divide by a negative number?
What happens when solving an inequality and you multiply or divide by a negative number?
How do you graph a linear inequality?
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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