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Untitled Quiz

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@SensationalChrysoprase468

Questions and Answers

What is the domain in relation to a function?

  • Any set of ordered pairs
  • Set of all inputs or independent variable values, x's (correct)
  • Ordered pairs where every x is paired with only one y
  • Set of all outputs or dependent variable values, y's

    • What is the range in relation to a function?

  • Set of all inputs or independent variable values, x's
  • Any set of ordered pairs
  • Set of all outputs or dependent variable values, y's (correct)
  • Ordered pairs where every x is paired with only one y

    • What is a relation?

    Any set of ordered pairs

    What is a function?

    <p>Ordered pairs where every x is paired with only one y</p> Signup and view all the answers

    What is the vertical line test?

    <p>Test to determine if a graph is a function</p> Signup and view all the answers

    How do you find the x-intercept of an equation when no points are given?

    <p>Find the value of x when y=0</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 is the standard form of a linear equation?

    <p>ax + by = c</p> Signup and view all the answers

    What is the best use for slope-intercept form?

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

    What is the best use for point-slope form?

    <p>Writing equations for lines</p> Signup and view all the answers

    What is the best use for standard form?

    <p>Finding x and y intercepts</p> Signup and view all the answers

    What is a linear sequence?

    <p>Sequence with constant difference between terms</p> Signup and view all the answers

    What is the graph of an arithmetic sequence?

    <p>Scatterplot with linear points and domain of counting numbers</p> Signup and view all the answers

    How do you find the first term if given the 10th and 20th term?

    <p>Find the ratio of term to term number</p> Signup and view all the answers

    What are the steps to solve using linear combination?

    <p>Put equations into standard form, find opposites, combine equations together, solve</p> Signup and view all the answers

    How do you write matrix equations?

    <p>[coefficients]*[variables in correct order] = [answers given without using calculator]</p> Signup and view all the answers

    What does the discriminant represent?

    <p>b^2 - 4ac</p> Signup and view all the answers

    What constitutes a polynomial?

    <p>Exponents are whole numbers and not x</p> Signup and view all the answers

    Describe the shape of the graph for x^2.

    <p>Bowl shape</p> Signup and view all the answers

    Describe the shape of the graph for x.

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

    Describe the shape of the graph for x^3.

    <p>Disco left to right</p> Signup and view all the answers

    Describe the shape of the graph for |x|.

    <p>V shape</p> Signup and view all the answers

    Describe the shape of the graph for the square root of x.

    <p>Stretch (arrow in upper right quadrant pointing to right)</p> Signup and view all the answers

    Describe the shape of the graph for b^x when b > 1.

    <p>Hill going down right to left (upper 2 quadrants)</p> Signup and view all the answers

    Study Notes

    Key Concepts in Advanced Algebra

    • Domain: Represents the complete set of inputs or values of the independent variable, typically denoted as x.

    • Range: Encompasses all possible outputs or values of the dependent variable, typically denoted as y.

    • Relation: Defined as any collection of ordered pairs.

    • Function: A special type of relation where each x-value is associated with exactly one y-value.

    • Vertical Line Test: A method to verify if a graph represents a function; a vertical line should intersect the graph at only one point.

    • Finding x-intercept: Determine the x-value where y equals zero.

    Forms of Linear Equations

    • Point-Slope Form: Expressed as (y - y_1 = m(x - x_1)), useful for writing equations based on one known point and the slope.

    • Standard Form: Written as (ax + by = c), typically used for identifying x and y-intercepts.

    • Slope-Intercept Form: Used primarily for graphing; represented as (y = mx + b), where m is the slope and b is the y-intercept.

    Sequences and Their Graphs

    • Linear Sequence: This involves a sequence with a constant difference between consecutive terms.

    • Graph of Arithmetic Sequence: Depicted as a scatterplot that forms linear points with a domain consisting of counting numbers.

    • Finding the First Term: To retrieve the first term from specified later terms (like the 10th and 20th terms), calculate the ratio of the changes between terms.

    Solving and Writing Equations

    • Linear Combination Steps: Start by placing equations in standard form, find opposite coefficients, combine the equations effectively, and then solve for the variable.

    • Writing Matrix Equations: Represented as ([coefficients] * [variables] = [answers]) while avoiding calculator use.

    Polynomial Characteristics

    • Discriminant: Given by the formula (b^2 - 4ac), key for determining the nature of roots in a quadratic equation.

    • Polynomial Degree: Identified as the highest exponent present in the polynomial.

    • Polynomial Criteria: An expression qualifies as a polynomial if all exponents are whole numbers.

    Graph Shapes

    • Quadratic Function (x^2): Typically forms a bowl shape.

    • Linear Function (x): Results in a straight line.

    • Cubic Function (x^3): Features a distinct "disco" pattern across the graph.

    • Absolute Value (|x|): Characterized by a V shape, displaying symmetry about the y-axis.

    • Square Root of x: Shows a stretched pattern, with an arrow pointing in the upper right quadrant.

    • Exponential Function (b^x) (b > 1): Descends in a "hill" shape sloping down from left to right in the upper two quadrants.

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