AND = Inverse Variation Graph: = Inverse Variation Graph: =
AND = Inverse Variation Graph: = Inverse Variation Graph: =
AND = Inverse Variation Graph: = Inverse Variation Graph: =
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2.6 <strong>Inverse</strong> <strong>Variation</strong> <strong>Graph</strong>s: y = k x <strong>AND</strong> y = k x 2SKILLS TO ACQUIRE: RECOGNIZE PROPERTIES OF THE GRAPHS GRAPH VARIATION EQUATIONVOCABULARY Branches: Parts of a graph (not linear!) Vertical Asymptote (VA): An imaginary vertical line that the graph gets close to but does notcross Horizontal Asymptote (HA): An imaginary horizontal line that the graph gets close to butdoes not cross<strong>Inverse</strong> <strong>Variation</strong> <strong>Graph</strong>: y = k XGRAPH: GRAPH: GRAPH:y = 1 and y = 4 y = 1 and y = 1 y = 1 −1and y =x xx 4xx xType of <strong>Graph</strong>: HyperbolaLINE OF SYMMETRY: y=x or y=-xVA: y-axisHA: x-axisNote: BRANCHES DIAGONAL0 < K < 1 or -1 < K < 0: graph closer to originK > 1: graph farther from originK>0:DOMAIN: x cannot be 0RANGE: y cannot be 0QUADRANTS: 1 and 3K
Go For It!Which of the four graphs match the following descriptions?There can be more than one answer!a) y = kx b) y = kx 2 c) y=k/x d) y=k/x 21.) Two lines of symmetry?2.) Asymptotes?3.) When K < 0, have graphs in the first quadrant?4.) Is a hyperbola?5.) Constant slope?6.) Has a domain of all real numbers?7.) Has a range of all real numbers except 0?8.) Has its branches side by side?9.) When K > 0, graph is in the 2 nd quadrant?10.) When K < 0, has a range y < 0.11.) Sketch the graph of y = 5 x12.) Sketch a graph of y = 15x 2
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