College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 8 - Summary, Review, and Test - Cumulative Review Exercises (Chapters 1-8) - Page 792: 1

Answer

Domain: $[-4,1)$ Range: $(-infinity, 2]$

Work Step by Step

$$Domain$$ The domain represents all the values of $x$ that the function $f(x)$ allows. In the exercise, the graph of $f(x)$ begins with point $(-4,0)$ and then continues. However, $f(x)$ is bound by a vertical asymptote which it cannot cross. Since there is no graph of $f(x)$ on the other side of the asymptote, we are forced to conclude that $f(x)$ is defined only until $x=1$ without including said value. Therefore, the Domain of $f(x)$ is {$x| -4\leq x\lt1$, where $x$ belongs to the realm of Real numbers}, also expressed as $[-4, 1)$ because it includes -4 but not 1. $$Range$$ The Range, on the other hand, represents all the values of $f(x)$ that result from the function's domain. From the function's graph, we observe that it's highest value on the vertical axis is $2$ before descending unto negative infinity. Therefore, the range of the function can be expressed as $(-infinity, 2]$ since the value 2 is included in $f(x)$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.