Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.2 - Graphs of Functions - 2.2 Exercises - Page 167: 33

Answer

f(x)=0 is represented as a red line. Note that since the limitation given is x$\lt $2, the point at (2,0) is actually (2,undefined) and has a hole. f(x)=1 is represented as a blue line. Note that since the limitation given is x$\geq$ 2, the point at (2,1) is a filled in point since the limitation is greater than or EQUAL to 2.

Work Step by Step

When looking at the problem, initially look at the limitations. The limitations will tell you if there is a break in the functions. In this example, f(x)=0 is limited by x$\lt$ 2. This means that there will be an open hole at (2, 0(undefined)) due to the less than symbol. For the other portion of the equation, f(x)= 1 is limited by x$\geq $2. This means that there is a closed hole at (2,1) because the limitation is "created than or EQUAL to 2." Given this, you follow your function rules and graph the equation.
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