Podcast
Questions and Answers
What are whole numbers?
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?
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?
What is a rational number?
Any number that can be written as a fraction
What defines an irrational number?
What defines an irrational number?
What are opposites?
What are opposites?
What does absolute value represent?
What does absolute value represent?
What is a function?
What is a function?
What is the zero of a function?
What is the zero of a function?
What are the domain and range of a function?
What are the domain and range of a function?
What is the vertical line test?
What is the vertical line test?
What is slope-intercept form?
What is slope-intercept form?
What is the standard form of a linear equation?
What is the standard form of a linear equation?
What is point-slope form of an equation?
What is point-slope form of an equation?
What is an x-intercept?
What is an x-intercept?
What is a y-intercept?
What is a y-intercept?
What defines a horizontal line?
What defines a horizontal line?
What defines a vertical line?
What defines a vertical line?
What are parallel lines?
What are parallel lines?
What are perpendicular lines?
What are perpendicular lines?
What is the slope formula?
What is the slope formula?
What is direct variation?
What is direct variation?
What do you need to do when solving an inequality?
What do you need to do when solving an inequality?
How do you graph inequalities on a number line?
How do you graph inequalities on a number line?
What are absolute value equations?
What are absolute value equations?
How do you interpret absolute value inequalities?
How do you interpret absolute value inequalities?
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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