Exam 12: Polynomial Functions of Higher Degree

An open box is to be made from a square piece of cardboard,33 inches on a side,by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function,V,in terms of x,that represents the volume of the box.

Select the correct graph of the function.​ $y = 2 x ^ { 3 } - 24 x ^ { 2 } + 36 x$ ​

Select from the following which is the polynomial function that has the given zeros.​ $5 , - 7$ ​

Select the graph of $y = x ^ { 3 }$ and the transformation $f ( x ) = ( x - 3 ) ^ { 3 }$ . ​

Select the correct graph of the functions f and g which shows the right-hand and left-hand behaviors of f and g appear identical.​ $f ( x ) = - \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 16 x \right)$ , $g ( x ) = - 4 x ^ { 4 }$ ​

Select from the following which is the polynomial function that has the given zeros.​ $- 4 , - 2,0,2,4$ ​

Select from the following which is the polynomial function that has the given zeros.​ $0,5$ ​

Select the graph of the function and use the zero or root feature to approximate the real zeros of the function.​ $f ( x ) = \frac { 1 } { 8 } x ^ { 4 } - 4 x ^ { 2 }$ ​

Graph the polynomial function.​ $y = - x ^ { 3 } + 3$ ​

Find a polynomial with the given zeros.​ $1,1,7$ ​

Select the graph of $y = x ^ { 4 }$ and the transformation $f ( x ) = \left( \frac { 1 } { 2 } x \right) ^ { 4 } - 2$ . ​

Select the correct graph of the function.​ $y = x ^ { 5 } - 5 x ^ { 3 } + 3 x$ ​

Select the graph of $y = x ^ { 6 }$ and the transformation $f ( x ) = ( x + 3 ) ^ { 6 }$ . ​

Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function.​ $f ( x ) = \frac { 1 } { 2 } x ^ { 3 } + 3 x$ ​

A roofing contractor is fabricating gutters from $10$ -inch aluminum sheeting.The contractor plans to use an aluminum siding folding press to create the gutter by creasing equal lengths for the sidewalls (see figure). ​ where $a = 10 - 2 x$ Let x represent the height of the sidewall of the gutter.Write a function A that represents the Cross-sectional area of the gutter. ​

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

Select the graph of the function and determine the zeros of the polynomial.​ $f ( t ) = \frac { 1 } { 6 } \left( t ^ { 2 } - 2 t + 20 \right)$ ​

Select the graph of the function and determine the zeros of the polynomial.​ $f ( x ) = x ^ { 2 } ( x - 5 )$ ​

Select from the following which is the polynomial of degree n that has the given zero(s). ​ Zero Degree $x = - 7$ $n = 2$ ​ ​

Find a polynomial with the given zeros.​ $0,0,0 , \sqrt { 3 } , - \sqrt { 3 }$ ​