Questions and Answers
Hver er merkingin með m í jöfnu línu y = mx + b?
Hvað segir jafnan (x - h)² + (y - k)² = r² til um hring?
Hvað gerist þegar graf er hliðrað?
Hver eru eiginleikar stranglega minnkandi falls?
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Hver er helsti eiginleiki jafnstæða falls?
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Hvað lýsir best aðferðinni við að finna rætur margliða?
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Hver er munurinn á tölugildisfallinu og venjulegum föllum?
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Hvernig skali við graf til að breyta stærð þess?
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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.
