Exam 2: Polynomial, Power, and Rational Functions

Describe how to transform the graph of an appropriate monomial function f(x) = xn into the graph of the given polynomial function. Then sketch the transformed graph. - $g ( x ) = 2 ( x - 4 ) ^ { 4 } + 2$

Determine if the function is a power function. If it is, then state the power and constant of variation. - $\mathrm { S } = 4 \pi \mathrm { r } ^ { 2 }$

Solve the problem. -Consider all rectangles with an area of $256 \mathrm {~cm} ^ { 2 }$ . Let $x$ be the length of one side of such a rectangle. Express the perimeter as a function of $x$ and determine the dimensions of the rectangle that has the least perimeter.

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth. - $f ( x ) = x ^ { 4 } + 4.87 x ^ { 3 } + 16.17 x ^ { 2 } + 10.08 x - 4.00$

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. - $x + 3 ; 7 x ^ { 4 } + 22 x ^ { 3 } - 3 x ^ { 2 } + x + 4$

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } + 2 x + 4 ; d ( x ) = x ^ { 2 } + 1 \quad$ (Write answer in fraction form)

Solve the problem. -The first column shows the independent variable $( x )$ . The second column shows the dependent variable $( y )$ . Use linear regression to predict the value of $y$ when $x = 7.1$ .

Write an equation for the quadratic function whose graph contains the given vertex and point. - (Write your answer in vertex form.)

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 9 x + 14$

Solve the problem. -An open-top rectangular box has a square base and it will hold 105 cubic centimeters (cc). Each side has length $x$ $\mathrm { cm }$ , and it has a height of $\mathrm { y } \mathrm { cm }$ . Express the surface area as a function of the length $x$ of a side of the base.

Find a cubic function with the given zeros. - $4 , - 2,5$

Find the vertex of the graph of the function. - $f ( x ) = ( x - 3 ) ^ { 2 } - 2$

Determine if the function is a power function. If it is, then state the power and constant of variation. - $f ( x ) = 5 x ^ { 3 / 7 }$

Find the vertex of the graph of the function. - $f ( x ) = ( x - 7 ) ^ { 2 } + 2$

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 7 x - 14$

Find the axis of the graph of the function. - $f ( x ) = 7 x ^ { 2 } - 112 x + 458$

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

Find the zeros of the function. - $f ( x ) = x ^ { 3 } - 17 x ^ { 2 } + 94 x - 168$

Match the polynomial function graph to the appropriate zeros and multiplicities. -