Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.1 - Graphs and Models - Exercises - Page 9: 71

Answer

a) $k=4$; b) $k=-1/8$; c) $k$ can be any real number; d) $k=1$.

Work Step by Step

In all of the parts we substitute for $y$ the second coordinate of the point and for $x$ the first coordinate of the point into the equation $y=kx^3$ and then we calculate k. a) $$4=k\times1^3\Rightarrow 4=k$$ So here for $k=4$ the graph passes through point $(1,4)$. b) $$1=k\times(-2)^3 \Rightarrow 1=k\times (-8)\Rightarrow k = -\frac{1}{8}$$ so for $k=-1/8$ the graph passes through $(-2,1)$. c) $$0=k\times 0^3\Rightarrow 0=k\times 0.$$ The last equation is true for any $k$ so for every real value of $k$ the graph will certainly pass through $(0,0)$. d) $$-1=k\times(-1)^3\Rightarrow -1=-k\Rightarrow k=1$$ so for $k=1$ the graph will pass through $(-1,-1)$.
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