Algebra Class: Rational Numbers and Functions
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Questions and Answers

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?

  • 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?

    Each input is paired to exactly one output.

    What is the zero of a function?

    <p>x-intercept where f(x) equals zero.</p> Signup and view all the answers

    What does 'domain' refer to in mathematics?

    <p>Input or x-values.</p> Signup and view all the answers

    What does 'range' refer to in mathematics?

    <p>Output or y-values.</p> Signup and view all the answers

    What is the vertical line test used for?

    <p>To determine if a graphed relation is a function.</p> Signup and view all the answers

    Linear equations have multiple outputs for the same input.

    <p>False</p> Signup and view all the answers

    What is the slope-intercept form of a line?

    <p>y = mx + b.</p> Signup and view all the answers

    What is the standard form of a linear equation?

    <p>Ax + By = C.</p> Signup and view all the answers

    What is the point-slope form of a linear equation?

    <p>y - y1 = m(x - x1).</p> Signup and view all the answers

    What are parallel lines?

    <p>Two lines that have the same slope.</p> Signup and view all the answers

    What are perpendicular lines?

    <p>Two lines with opposite reciprocal slopes.</p> Signup and view all the answers

    What is direct variation?

    <p>y = kx where k is the constant of variation.</p> Signup and view all the answers

    What happens when solving an inequality and you multiply or divide by a negative number?

    <p>Reverse the inequality sign.</p> Signup and view all the answers

    How do you graph a linear inequality?

    <p>Graph the boundary line with solid or dotted lines depending on the inequalities.</p> 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).

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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.

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