Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.1 - Real Numbers - 1.1 Exercises: 53


($-\infty, 1$]

Work Step by Step

The set $x \leq 1$ means $x$ can be any value that is less than or equal to one. In terms of interval notation, this means it can be from negative infinity to one, including one. To write this, you go from $- \infty$ to 1 with $-\infty, 1$ and then add a left parenthesis in front of the infinity (because infinity is not a number and therefore is never square bracketed), and a right square bracket to the right of the one to show that it is included. To graph this on a number line, you start with a closed point at 1 to show that it can equal one, and then shade towards the negative side (left). Because it goes to infinity in this direction, add an arrow to the left end of the line.
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