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. - $g ( x ) = 5 ( x + 3 ) ^ { 4 } + 2$

Find the axis of the graph of the function. - $f ( x ) = 4 x ^ { 2 } + 40 x + 96$

Solve the polynomial inequality. - $( x - 3 ) \left( x ^ { 2 } - 3 x - 10 \right) < 0$

Write the statement as a power function equation. Use k as the constant of variation. - $x$ varies directly as $y$ .

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. - $k = 5 ; f ( x ) = 3 x ^ { 3 } - 3 x ^ { 2 } + 5 x - 2 ;$ Upper bound?

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { 2 x } { x + 2 } + \frac { 5 } { x - 5 } = \frac { 8 } { x ^ { 2 } - 3 x - 10 }$

Find the requested function. -Find the polynomial function with leading coefficient 3 ; degree 3 ; and $- 3,4$ , and $\frac { 2 } { 3 }$ as zeros.

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. - $\mathrm { I } ( \mathrm { d } ) = \frac { \mathrm { k } } { \mathrm { d } ^ { 2 } }$

Solve the polynomial inequality. - $( x + 9 ) ( x + 3 ) ( x - 4 ) < 0$

Match the equation to the correct graph. - $f ( x ) = - 3 + 3 ( x - 2 ) ^ { 2 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros: $- 2,1,0 ; f ( 2 ) = 40$

Find the zeros of the function. - $f ( x ) = 3 x ^ { 2 } + 17 x + 20$

Determine whether the power function is even, odd, or neither. - $f ( x ) = \frac { 1 } { 2 } x ^ { - 9 }$

Divide using synthetic division, and write a summary statement in fraction form. - $\frac { 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x } { x + 3 }$

Find the axis of the graph of the function. - $f ( x ) = 4 x ^ { 2 } + 32 x + 65$

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = ( x + 1 ) ^ { 2 } ( x - 1 ) ( x - 2 )$

Divide using synthetic division, and write a summary statement in fraction form. - $\frac { 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 } { x + 2 }$

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - $f ( x ) = ( x + 7 ) ( x + 5 ) ( x - 7 ) ^ { 2 }$

Match the graph of the rational function with its equation. -

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth. - $f ( x ) = 2 x ^ { 4 } + 4 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 1$