College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.1 - Functions - 2.1 Exercises: 54

Answer

Domain: $[0,2]$ Range: $[4,24]$

Work Step by Step

We are given: $f(x)=5x^{2}+4, 0\leq x\leq 2$ The domain consists of all values that $x$ is allowed to be. In this case, $x$ is restricted to fall between $0$ and $2$, so the domain is: $[0, 2]$. The range consists of all values that $y$ can be. We find the extremes of $y$ by using the end points of $x$ (this works because the equation is a parabola): $f(0)=5(0)^{2}+4=4$ $f(2)=5(2)^{2}+4=24$ Thus the range is: $[4, 24]$.
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