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21 votes
21 votes
6. Find the domain and range of V(x) in this context.7. Think of V(x) as a general function without the constraint of modeling the volume of a box. What would be the domain and range of V(x)?8. Use correct notation to describe the end behavior of V(x) as a function without context.

6. Find the domain and range of V(x) in this context.7. Think of V(x) as a general-example-1
User Lolindrath
by
2.5k points

1 Answer

16 votes
16 votes

We have , that measure of the side of the square is x

Therefore

l=26-2x

w=20-2x

h=x

Therefore the Volume function is


V=(26-2x)(20-2x)x

Then we simplify


V(x)=4x^3-92x^2+520x

6.In the context of obtaining a Volume we can't have negative numbers for x and for the function by observing the graph

Domain


0\le x\le10

Therefore for the range


0\: 7.<p>Because we have a polynomial</p><p></p><p>the domain without the constrain</p>[tex]-\infty\: the range without the constrain<p></p>[tex]-\infty\: 8.<p>Since the leading term of the polynomial is 4 x^(3), the degree is 3, i.e. odd, and the leading coefficient is 4, i.e. positive. This means</p>[tex]\begin{gathered} x\to-\infty,\text{ }f(x)\to-\infty \\ x\to\infty,f(x)\to\infty \end{gathered}

6. Find the domain and range of V(x) in this context.7. Think of V(x) as a general-example-1
User Lachezar Todorov
by
2.9k points
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