Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.2 Representing Functions - 1.2 Exercises - Page 22: 23


The graph is in the figure below

Work Step by Step

When $x\neq 1$ this is a linear function in disguise: $$f(x)=\frac{x^2-x}{x-1}=\frac{x(x-1)}{x-1}=x$$ and it was legal to cancel the term $x-1$ because $x\neq1$. So this function can be rewritten as $$f(x)=\bigg\{_{x,\quad x\neq1.}^{2,\quad x=1;}.$$ This function is given on the graph below where the filled circle says that the endpoint is included while the empty circle means that the endpoints are excluded
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