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Unformatted text preview: r function.
y= 1
x y x y=x 0 0 undefined 1
4 1
4 4 1
3 1
3 3 1
2 1
2 2 ( 1 ,4 )
4
( 1 ,3)
3
( 1 ,2)
2 1 1 1 (1,1) 2 2 1
2 3 3 1
3 4 4 1
4 no point
3 y= 1
x
3 (2, 1 )
2
(3, 1 )
3
( 4, 1 )
4 0 3 3 The function values for y = 1 are the reciprocals of the function values of y = x .
x
An asymptote is a line that a curve keeps getting closer to without ever reaching.
Function value of the
linear function y = x
0 Function value of the linear function's
reciprocal function y = 1
x
undefined; the reciprocal of 0 does not exist approaches 0 goes toward ∞ or −∞; there will be a vertical asymptote
where the linear function value is 0 1 or −1 1 or −1; these are invariant points since the "reciprocal
transformation" does not affect these points goes toward ∞ or −∞ approaches 0; if this happens at the far left and right end of
the graph there will be horizontal asymptotes at the ends x Unit 6: Day 4 notes  Reciprocal Functions (Part 1) Page 2 of 4 Remember to consider the domain and range of reciprocal functions. GRAPHING y = 1 , THE RECIPROCAL OF A LINEAR FUNCTION
ax + b example: Graph of y = 1
by transforming the graph of the linear function.
2x − 3 o Draw the graph of y = 2x − 3 y y = 2x − 3 4 o At the point on the linear graph with
ycoordinate 0, the reciprocal graph will not 2 have a point for that xvalue; there is probably
a vertical asymptote there. y= 1
2x − 3 2 2
2 o At the points on the linear graph with
ycoordinates approaching 0, the reciprocal
graph will have points with yvalues going to ∞ 4 or −∞; there is a vertical asymptote at the
linear function's xintercept. o At the points on the linear graph with ycoordinates 1 or −1, the reciprocal
graph will have the same points; these are invariant points. o At the points on the linear graph with ycoordinates going to ∞ or −∞; the
reciprocal graph will have points approaching the xaxis; the xaxis is a
horizontal asymptote for the left and right ends of the reciprocal graph. What is the nonpermissible value of ratio...
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 Fall '11
 Aytona
 Calculus, PreCalculus

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