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Questions and Answers

What are whole numbers?

  • -1, 0, 1, 2,...
  • 1, 2, 3,...
  • 0, 1, 2,... (correct)
  • Any positive number

Which of the following lists shows the integers?

  • All positive numbers
  • -3, -2, -1, 0, 1, 2, 3,... (correct)
  • 0, 1, 2,...
  • 1, 2, 3,...

What is a rational number?

Any number that can be written as a fraction

What defines an irrational number?

<p>Any number that cannot be written as a fraction</p> Signup and view all the answers

What are opposites?

<p>A and -A</p> Signup and view all the answers

What does absolute value represent?

<p>Distance between a number and zero</p> Signup and view all the answers

What is a function?

<p>Each input is paired with exactly one output</p> Signup and view all the answers

What is the zero of a function?

<p>X-intercept</p> Signup and view all the answers

What are the domain and range of a function?

<p>Domain refers to input or X-values, while range refers to output or Y-values.</p> Signup and view all the answers

What is the vertical line test?

<p>A method to determine if a graphed relation is a function</p> Signup and view all the answers

What is slope-intercept form?

<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 point-slope form of an equation?

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

What is an x-intercept?

<p>Where the graph crosses the x-axis</p> Signup and view all the answers

What is a y-intercept?

<p>Where the graph crosses the y-axis</p> Signup and view all the answers

What defines a horizontal line?

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

What defines a vertical line?

<p>x = a</p> Signup and view all the answers

What are parallel lines?

<p>Two lines with 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 the slope formula?

<p>Δy/Δx = (y₂ - y₁) / (x₂ - x₁)</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 do you need to do when solving an inequality?

<p>Reverse the inequality sign if you multiply or divide by a negative number</p> Signup and view all the answers

How do you graph inequalities on a number line?

<p>Use dashed lines for 'less than' or 'greater than', and choose test points to determine shading.</p> Signup and view all the answers

What are absolute value equations?

<p>|x|=a signifies x=a or x=-a</p> Signup and view all the answers

How do you interpret absolute value inequalities?

<p>Less than forms 'and' compound inequalities.</p> Signup and view all the answers

Study Notes

Whole Numbers

  • Defined as 0, 1, 2, 3, and so on.

Integers

  • Include negative and positive whole numbers: -3, -2, -1, 0, 1, 2, 3, etc.

Rational Numbers

  • Can be expressed as a fraction (e.g., proper and improper fractions, mixed numbers, terminating and repeating decimals).
  • Includes integers and whole numbers.

Irrational Numbers

  • Cannot be represented as a fraction.
  • Example includes decimal numbers that repeat without a pattern.

Opposites

  • For any number A, its opposite is -A (e.g., -5 is the opposite of 5).

Absolute Value

  • Represents the distance of a number from zero; always a positive value.

Functions

  • Each input corresponds to exactly one output, ensuring no repeated input values.

Zero of a Function

  • The x-intercept found when y (or f(x)) is equal to zero.

Domain

  • Represents the set of input values (or x-values).

Range

  • Represents the set of output values (or y-values).

Vertical Line Test

  • Determines if a graphed relation is a function by checking if a vertical line passes through more than one point.

Slope-Intercept Form

  • Expressed as y = mx + b, where m is the slope and b is the y-intercept.

Standard Form

  • Written as Ax + By = C, where A, B, and C are integers.

Point-Slope Form

  • Defined as y - y₁ = m(x - x₁); m is the slope and (x₁, y₁) is a point on the line.

X-Intercept

  • The point where a graph crosses the x-axis, represented as (x, 0).
  • Found by setting y = 0.

Y-Intercept

  • The point where a graph crosses the y-axis, represented as (0, y).
  • Found by setting x = 0.

Horizontal Line

  • Defined by the equation y = b, where all points have the same y-value.

Vertical Line

  • Defined by the equation x = a, where all points have the same x-value.

Parallel Lines

  • Two lines with identical slopes, indicating they will never intersect.

Perpendicular Lines

  • Two lines with slopes that are opposite reciprocals (e.g., a slope of 3 has a perpendicular slope of -1/3).

Slope Formula

  • Calculated as Δy/Δx or (y₂ - y₁)/(x₂ - x₁).

Direct Variation

  • Describes a relationship y = kx, where k is the constant of variation (slope).
  • Graphically represented as a line that always passes through the origin.

Solving an Inequality

  • When multiplying or dividing both sides by a negative number, the inequality sign must be reversed.

Graphing Inequalities on a Number Line

  • Use a dashed line for "less than" or "greater than" inequalities and a solid line for "less than or equal to"/"greater than or equal to."
  • Determine which side to shade with a test point; overlapping regions signify the solution in linear systems.

Absolute Value Equations

  • E.g., |x| = 4 results in x = 4 or x = -4. If |x| = no solution, the equation has no valid x-value.

Absolute Value Inequalities

  • "Less than" creates an "and" compound inequality: |x| < k leads to two inequalities: -k < x < k.

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