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Unformatted text preview: nal expression What is the domain of the reciprocal function y = What is the range of the reciprocal function y = 1
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2x − 3 1
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2x − 3 1
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2x − 3 x Unit 6: Day 4 notes  Reciprocal Functions (Part 1) Page 3 of 4 1 ; determine nonpermissible values, the domain, and the range
2−x
before graphing the function. exercise: y = [Answer: x ≠ 2 ; {x x ≠ 2, x∈R}; {y y ≠ 0, y∈R}] y 1
by
2−x
transforming the graph of the linear
function. exercise: Draw the graph of y = 3 3 0 3 x 3 x 3 y exercise: Draw the graph of y = 1 by
f ( x)
transforming the graph of 3 2 if x > 2 f (x) = x if − 2 ≤ x ≤ 2 −2 if x < −2 3 0 3 Unit 6: Day 4 notes  Reciprocal Functions (Part 1) GRAPHING y = 1
a ( x − p)2 + q Page 4 of 4 , THE RECIPROCAL OF A QUADRATIC FUNCTION example: Draw the graph of y = 1
.
x − 4x + 3
2 y y = x2 − 4x + 3 o Draw the graph of y = (x − 2)2 − 1 It's vertex equation is
The vertex is (2,−1) 2 It's factored form is
y = (x − 1)(x − 3)
The xintercepts are (1,0) and (3,0) 0 2 4 x 2 o At the points on the quadratic graph with
ycoordinate 0, the reciprocal graph will not
have a point for that xvalue.
o At the points on the quadratic graph with ycoordinates approaching 0, the
reciprocal graph will have points with yvalues going to ∞ or −∞; there are
vertical asymptotes at the quadratic function's xintercepts.
o At the points on the quadratic graph with ycoordinates 1 or −1, the
reciprocal graph will have the same points; these are invariant points.
o At the points on the quadratic 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. exercise: Draw the graph of y = y 1
x −4
2 3 3 0 3 3 x PRECALCULUS 11 Unit 6 – Day 5: RECIPROCAL FUNCTIONS (Part 2) MODELLING PROBLEMS WITH RECIPROCAL FUNCTIONS
There are pairs of quantities that are reciprocals. One well known pair of reciprocal
quantities are frequency and period.
F...
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This document was uploaded on 02/16/2014 for the course MATH PreCalcul at Holy Cross Regional High School.
 Fall '11
 Aytona
 Calculus, PreCalculus

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