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?
Signup and view all the answers
What does 'domain' refer to in mathematics?
Signup and view all the answers
What does 'range' refer to in mathematics?
Signup and view all the answers
What is the vertical line test used for?
Signup and view all the answers
Linear equations have multiple outputs for the same input.
Signup and view all the answers
What is the slope-intercept form of a line?
Signup and view all the answers
What is the standard form of a linear equation?
Signup and view all the answers
What is the point-slope form of a linear equation?
Signup and view all the answers
What are parallel lines?
Signup and view all the answers
What are perpendicular lines?
Signup and view all the answers
What is direct variation?
Signup and view all the answers
What happens when solving an inequality and you multiply or divide by a negative number?
Signup and view all the answers
How do you graph a linear inequality?
Signup and view all the answers
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).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.