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Example Question #8 : Graphing Hyperbolic Inequalities
Which inequality does this graph represent?
The equation for a horizontal hyperbola is . The equation for a vertical hyperbola is
. In both, (h, v) is the center of the hyperbola. Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. The graph shows a vertical hyperbola, so in its corresponding inequality the y-term must appear first. The center is (0, 0), so neither x nor y can be followed by a constant. The center is shaded, so the left side of the graph’s corresponding inequality (the side containing the variables x and y) is less than the constant on the right side. The lines are solid rather than dashed, so the inequality sign must be
rather than
.
Example Question #9 : Graphing Hyperbolic Inequalities
Which graph represents the inequality ?
The equation for a horizontal hyperbola is. The equation for a vertical hyperbola is
. In both, (h, v) is the center of the hyperbola. Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. Neither the x nor the y in the inequality are followed by constants, so the graph must be centered on (0,0). The x-term appears first, so the graph must show a horizontal hyperbola. The inequality sign is
rather than
, so the lines must be dashed rather than solid. The left side is less than rather than greater than the constant, so the center must be shaded.
Example Question #10 : Graphing Hyperbolic Inequalities
Which graph represents the inequality ?
The equation for a horizontal hyperbola is . The equation for a vertical hyperbola is
. In both, (h, v) is the center of the hyperbola. Hyperbolic inequalities use an inequality sign rather than an equals sign, but otherwise have the same form as hyperbolic equations. The x and y in the inequality are followed by the constants 2 and -1 respectively, so the graph must be centered on (-2, 1). The y-term appears first, so the graph must show a vertical hyperbola. The inequality sign is
rather than
, so the lines must be solid rather than dashed. The left side is greater than rather than less than the constant, so the center must not be shaded.
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