Algebra 10: Jafna línu og hrings
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Questions and Answers

Hver er merkingin með m í jöfnu línu y = mx + b?

  • M er x-gildi jöfnunnar.
  • M er y-gildi jöfnunnar.
  • M er radíus hringins.
  • M er halla línunnar. (correct)

    • Hvað segir jafnan (x - h)² + (y - k)² = r² til um hring?

  • Miðpunktur hringsins er (h, k). (correct)
  • Hringurinn hefur engin rök.
  • Radíus hringsins er h.
  • Hringurinn er alltaf fullkominn.

    • Hvað gerist þegar graf er hliðrað?

  • Grafin breytast í flóknari graf.
  • Graf færist upp/niður eða til hægri/vinstri. (correct)
  • Graf hækkar alltaf í y-gildum.
  • Graf breytist í nýtt fall.

    • Hver eru eiginleikar stranglega minnkandi falls?

    <p>Gildi þess lækkar alltaf þegar x stækkar.</p> Signup and view all the answers

    Hver er helsti eiginleiki jafnstæða falls?

    <p>Föllin lítur eins út báðum megin við y-ás.</p> Signup and view all the answers

    Hvað lýsir best aðferðinni við að finna rætur margliða?

    <p>Rætur eru þau x-gildi þar sem margliðan er 0.</p> Signup and view all the answers

    Hver er munurinn á tölugildisfallinu og venjulegum föllum?

    <p>|x| er alltaf jákvætt, óháð því hvort x sé jákvætt eða neikvætt.</p> Signup and view all the answers

    Hvernig skali við graf til að breyta stærð þess?

    <p>Skölun eykur eða minnkar stærð grafins.</p> Signup and view all the answers

    Study Notes

    Equation of a Line

    • Describes the representation of a straight line in a graph.
    • The formula is y = mx + b.
    • m indicates the slope (direction of the line), determining if it rises or falls.
    • b is the y-intercept, indicating where the line crosses the y-axis.

    Equation of a Circle

    • Defines the graphical representation of a circle.
    • The formula is (x - h)² + (y - k)² = r².
    • (h, k) represents the center of the circle.
    • r is the radius, measuring the distance from the center to any point on the circumference.

    Translation and Scaling of Graphs

    • Translation shifts the graph horizontally or vertically without altering its shape.
    • Scaling enlarges or reduces the size of the graph, affecting its dimensions but not its structure.

    Strictly Decreasing and Increasing Functions

    • An increasing function rises as x increases.
    • A decreasing function falls as x increases.
    • Strictly implies that these behaviors consistently occur without exceptions.

    Even and Odd Functions

    • An even function has symmetry across the y-axis, appearing identical on both sides.
    • An odd function displays rotational symmetry about the origin, flipping at the ends.

    Polynomials; Division, Factoring, and Roots

    • Polynomials consist of several terms, e.g., x² + 3x + 2.
    • Methods like division and factoring are used to discover roots.
    • Roots are the specific values that result in the equation equating to zero.

    Absolute Value Function

    • The absolute value function measures the distance of a number from zero.
    • It is always non-negative, denoted as |x|; for instance, |−3| = 3.

    Triangle Inequality

    • States that the sum of any two sides of a triangle is always greater than the third side.
    • This principle establishes limits on the possible lengths of triangle sides.

    Sign Function (sgn(x))

    • Determines whether a number is positive, negative, or zero.
    • Outputs: sgn(x) = 1 if positive, sgn(x) = −1 if negative, and sgn(x) = 0 if zero.

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    Description

    Þetta kvizz fer í gegnum jöfnu línu og jöfnu hrings. Þú munt læra um hvernig þessi jöfnur eru samdar og hvað öll þættir þeirra þýða. Kannaðu halla línunnar og miðju hringsins.

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