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Chapter 2: Problem 29

Describe the right-hand and left-hand behavior of the graph of the polynomial function. \(h(t)=-\frac{3}{4}\left(t^{2}-3 t+6\right)\)

Short Answer

Expert verified
The graph of the given polynomial function points downwards on both ends. Therefore, as \(t\) approaches either positive or negative infinity, \(h(t)\) will approach negative infinity.

Step by step solution

01

Identify Degree and Leading Coefficient

The degree of the given polynomial \(h(t) = -\frac{3}{4} \left(t^{2}-3 t+6\right)\) is 2, which is even. The leading coefficient is -3/4, which is negative.
02

Determine End Behavior

As the degree is even and the leading coefficient is negative, both ends of the graph point downwards. This means that as \(t\) approaches positive or negative infinity, \(h(t)\) will approach negative infinity.

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