Reciprocal Graphs Sketch and hence find the reciprocal graph y = 0 y = 1 y = 2 y = 1/2 y = 3 y = 1/3...
3
Reciprocal Graphs Sketch and hence find the reciprocal graph () y fx 1 () y fx () y fx y = 0 y = 1 y = 2 y = 1/2 y = 3 y = 1/3 x = 1 y = 0 1 () y fx Hyperbola Asymptote Asymptote Domain: x R\{1} Range: y R\{0} Asymptotes: x = 1 y = 0 y-intercept y = 1
Reciprocal Graphs Sketch and hence find the reciprocal graph y = 0 y = 1 y = 2 y = 1/2 y = 3 y = 1/3 x = 1 y = 0 Hyperbola Asymptote Domain: x R\{1}
Reciprocal Graphs Sketch and hence find the reciprocal graph y
= 0 y = 1 y = 2 y = 1/2 y = 3 y = 1/3 x = 1 y = 0 Hyperbola
Asymptote Domain: x R\{1} Range: y R\{0} Asymptotes: x = 1 y = 0
y-intercept y = 1
Slide 3
Reciprocal Graphs All reciprocal graphs have a horizontal
asymptote along the x-axis (y = 0) Where the original graph has an
x-intercept (y-value = 0), there will be a vertical asymptote.
(Draw in and label) Where y-value = 1 (or 1), the reciprocal is
also 1 (or 1), so the graph and its reciprocal will intersect at
those points Where y-value > 1, reciprocal < 1 Where y-value
1 Where original graph is negative, reciprocal is also negative A
turning point not on the x-axis will create a turning point at the
same x- coordinate in the reciprocal graph. Pay attention to each
end of x-axis and close to vertical asymptotes Graphs should
approach but not touch asymptotes and they should not curl away
from asymptotes. State domain, range, equations of asymptotes,
intercepts, turning points
Slide 4
Reciprocal Graphs (2) Sketch and hence find the reciprocal
graph y = 0 x = 1 x = 3 tp = (2, 1) Domain: x R\{1, 3} Range: {y 1}
{y > 0} Asymptotes: y = 0 x = 1 x = 3 Stationary Point (2, 1)
lcl max Y-intercept y = 1/3