Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Mid-Chapter Check Point - Page 381: 16


The zeros of $f\left( x \right)=-{{\left( x+1 \right)}^{6}}$ are $-1,-1,-1,-1,-1,-1$.

Work Step by Step

Let’s first equate $f\left( x \right)$ to $0$. So, $-{{\left( x+1 \right)}^{6}}=0$ It can also be written as: $-\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)=0$ So, the zero of the provided function is $x=-1$ with the multiplicity of $6$. The graph touches the x- axis and turns around at $-1$ since it has multiplicity 6. Also, since the function is an even-degree polynomial and the leading coefficient is $-1$, the graph will fall downwards.
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