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 (B)</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

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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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