Exam 12: Polynomial Functions of Higher Degree

The growth of a red oak tree is approximated by the function ​​ $G = - 0.003 t ^ { 3 } + 0.137 t ^ { 2 } + 0.458 t - 0.839$ ​ Where G is the height of the tree (in feet)and t $( 2 \leq t \leq 34 )$ is its age (in years). Select the correct graph of the function. ​

Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function.​ $h ( t ) = t ^ { 2 } - 14 t + 49$ ​

Find all the real zeros of the polynomial function.​ $f ( x ) = x ^ { 2 } - 9$ ​

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20$ and determine the multiplicity of each.

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - 5 x ^ { 4 } + 12 x ^ { 3 } + 13$ .

Select the graph of $y = x ^ { 5 }$ and the transformation $f ( x ) = 1 - \frac { 1 } { 2 } x ^ { 5 }$ . ​

Using a graphing utility,graph $f ( x ) = x ^ { 5 } - 14 x ^ { 4 } + 49 x ^ { 3 }$ and approximate the zeros and their multiplicity.

An open box is to be made from a square piece of cardboard,24 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).If the volume of the box is represented by $V ( x ) = x ( 24 - 2 x ) ^ { 2 }$ ,determine the domain of $V ( x )$ .

Using a graphing utility,graph $f ( x ) = x ^ { 3 } - 4 x$ and approximate the zeros and their multiplicity.

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function.​ $g ( x ) = \frac { 1 } { 5 } ( x + 1 ) ^ { 2 } ( x - 3 ) ( 2 x - 7 )$ ​

The graph of the function g(x)is a translation of the graph of f (x)= x ³.Graph the function g(x)= (x - 3)³ - 1. ​

Select the graph of the function and determine the zeros of the polynomial.​ $f ( x ) = x ^ { 3 } - 25 x$ ​

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.​ $f ( t ) = 2 - 5 x + 3 x ^ { 2 } - 5 x ^ { 3 }$ ​

An open box is to be made from a square piece of cardboard, $66 \text { inches }$ on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V,in terms of x,that represents the volume of the box,use a graphing utility to estimate the dimensions that will maximize its volume.

An open box is to be made from a square piece of material,38 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure)​ ​ where $a = 38 - 2 x$ . Determine the domain of the following function,V(x)represents the volume of the box .​ $V ( x ) = x ( 38 - 2 x ) ^ { 2 }$ ​

Select the correct graph of the function.​ $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 1 } { 3 } x - \frac { 8 } { 3 }$ ​

Find a polynomial with the given zeros.​ $- 1,5 , - \sqrt { 7 } , \sqrt { 7 }$ ​

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function.​ $f ( x ) = x ^ { 3 } - 4 x$ ​

Match the equation with its graph.​ $\frac { 1 } { 20 } \left( x ^ { 5 } - x ^ { 4 } - 5 x ^ { 3 } - x ^ { 2 } - 6 x \right)$

Select the correct graph of the functions f and g in the same viewing window.Zoom out sufficiently far to show that the right-hand and left-hand behaviors of f and g appear identical.​ $f ( x ) = x ^ { 3 } - 4 x + 1$ , $g ( x ) = x ^ { 3 }$ ​