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Untitled Quiz

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Questions and Answers

What are rational numbers?

a/b is rational if a and b are integers and b does not equal 0

What are irrational numbers?

numbers that are not rational (don't terminate or repeat)

What are real numbers?

the set containing all rational and irrational numbers

What is an equation?

<p>a statement that two expressions are equal; we solve them</p> Signup and view all the answers

What is an expression?

<p>symbol or string of symbols; we simplify</p> Signup and view all the answers

What is a function?

<p>a relation for which each input has exactly one output</p> Signup and view all the answers

What is a relation?

<p>a mapping or pairing of inputs and outputs; a set of ordered pairs</p> Signup and view all the answers

What is the domain of a function?

<p>set of input values</p> Signup and view all the answers

What is the range of a function?

<p>set of output values</p> Signup and view all the answers

What is the vertical line test?

<p>a relation is a function iff no vertical line intersects the graph of the relation at more than one point</p> Signup and view all the answers

What is function notation?

<p>f(x)=mx+b</p> Signup and view all the answers

What is a parent function?

<p>the most basic function in a family, for linear y=x, for quadratic y=x^2</p> Signup and view all the answers

What is a discrete function?

<p>scatter plot</p> Signup and view all the answers

What is a continuous function?

<p>has an infinite number of points, all infinitely close together</p> Signup and view all the answers

What is the slope equation?

<p>y2 - y1 / x2 - x1</p> Signup and view all the answers

What are the types of slopes?

<p>positive, negative, zero, undefined</p> Signup and view all the answers

What is a vertical line?

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

What is a horizontal line?

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

What defines parallel lines on a graph?

<p>same slope, different y-intercept</p> Signup and view all the answers

What defines perpendicular lines on a graph?

<p>negative reciprocal of slope, any y-intercept</p> Signup and view all the answers

What is point-slope form?

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

What is direct variation?

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

What is constant variation?

<p>the non-zero constant a in y=ax</p> Signup and view all the answers

What defines a direct variation line?

<p>slope of a with y intercept of zero</p> Signup and view all the answers

What is linear regression?

<p>modeling 2 variable equation with a linear equation</p> Signup and view all the answers

What is extrapolation?

<p>making a prediction using the model of something beyond the data set</p> Signup and view all the answers

What is interpolation?

<p>using a model of something to make a prediction of data in the set</p> Signup and view all the answers

What is a model in mathematics?

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

What does the correlation coefficient r indicate?

<p>if r=0, no correlation; if r=+-1, perfect correlation</p> Signup and view all the answers

What is the line of least squares?

<p>minimizes the square of distances from the data points to the line</p> Signup and view all the answers

What is the slope in line of least squares?

<p>m=nΣ(xy)-ΣxΣy/nΣ(x^2)-(Σx)(Σx)</p> Signup and view all the answers

What is the piecewise definition of absolute value?

<p>|x|= x, true if x is positive or =0; -x, if x is less than 0</p> Signup and view all the answers

What does y=|x|+k affect?

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

What does y=|x+k| affect?

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

What is the greatest integer function?

<p>[x]=greatest integer function</p> Signup and view all the answers

What is the floor function?

<p>|<em>x</em>|=floor function, opposite=cieling function (round up)</p> Signup and view all the answers

Study Notes

Basic Algebra Concepts

  • Rational Numbers: Represented as a/b where a and b are integers; b cannot be zero.
  • Irrational Numbers: Numbers that cannot be expressed as a fraction; they do not terminate or repeat.
  • Real Numbers: The complete set that includes both rational and irrational numbers.

Equations and Expressions

  • Equation: A mathematical statement asserting that two expressions are equal; solved to find unknown values.
  • Expression: A combination of symbols representing a quantity; simplified rather than solved.

Functions and Relations

  • Function: A specific type of relation where each input corresponds to one unique output.
  • Relation: A collection of inputs paired with outputs, often represented as ordered pairs.

Domain and Range

  • Domain: The set of all possible input values for a function.
  • Range: The set of all possible output values from a function.

Graphical Analysis

  • Vertical Line Test: A criterion to determine if a relation is a function; no vertical line should intersect a graph more than once.
  • Function Notation: Expressed typically as f(x) = mx + b, where m represents the slope and b the y-intercept.

Types of Functions

  • Parent Function: The simplest form of a function, with linear as y = x and quadratic as y = x².
  • Discrete Function: Represented graphically as a scatter plot.
  • Continuous Function: A function that includes an infinite number of points closely packed together.

Slope and Lines

  • Slope Equation: Calculated as (y2 - y1) / (x2 - x1).
  • Types of Slopes: Can be positive, negative, zero (horizontal), or undefined (vertical).
  • Vertical Line: Represented by the equation x = b.
  • Horizontal Line: Represented by the equation y = a.
  • Parallel Lines: Lines with the same slope but different y-intercepts.
  • Perpendicular Lines: Lines that intersect at a right angle; slopes are negative reciprocals.

Equation Forms

  • Point-Slope Form: Expressed as y - y1 = m(x - x1), representing a line's steepness at a point.
  • Direct Variation: In the form y = ax, where 'a' is a constant that indicates the variation rate.
  • Constant Variation: The non-zero constant 'a' in the direct variation equation.

Linear Models and Predictions

  • Direct Variation Line: Has slope 'a' with a y-intercept of zero.
  • Linear Regression: A method for modeling the relationship between two variables with a linear equation.
  • Extrapolation: Making predictions beyond the current dataset using established models.
  • Interpolation: Using a model to estimate data values within the existing dataset.

Additional Concepts

  • Model: A representation in equation form that describes a relationship.
  • Correlation Coefficient (r): Indicates the strength and direction of a linear relationship; r = 0 indicates no correlation, ±1 indicates perfect correlation.
  • Line of Least Squares: A line that minimizes the sum of the squared differences between observed values and the line.
  • Slope in Line of Least Squares: Determined through a specific formula involving sums of products and squared terms.
  • Piecewise Definition of Absolute Value: |x| = x if x ≥ 0; = -x if x < 0.
  • Transformations of Absolute Value Functions:
    • y = |x| + k: Affects the y-intercept.
    • y = |x + k|: Affects the x-intercept.
  • Greatest Integer Function: Denoted as [x], representing the largest integer less than or equal to x, also known as the floor function; its opposite is the ceiling function, which rounds up.

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