Exam 2: Polynomial, Power, and Rational Functions

Describe the end behavior of the polynomial function by finding - $f ( x ) = x ^ { 3 } - x ^ { 4 } - 7 x ^ { 2 } + 2 x + 8$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { 4 } { x + 4 } - \frac { 8 } { x - 4 } = \frac { 12 } { x ^ { 2 } - 16 }$

Find the axis of the graph of the function. - $f ( x ) = ( x - 5 ) ^ { 2 } - 5$

Solve the polynomial inequality. - $( 2 x + 7 ) ( x - 5 ) ( 3 x - 2 ) \leq 0$

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = ( 4 x + 1 ) ( x + 2 ) ^ { 3 }$

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

Write the polynomial in standard form and identify the zeros of the function. - $f ( x ) = ( x + 2 ) ( x + 2 ) ( x + 3 i ) ( x - 3 i )$

Solve the problem. -The perimeter of a rectangle is $78 \mathrm {~m}$ . If the width were doubled and the length were increased by $16 \mathrm {~m}$ , the perimeter would be $138 \mathrm {~m}$ . What are the length and width of the rectangle?

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

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

Write a linear factorization of the function. - $f ( x ) = x ^ { 4 } + 25 x ^ { 2 }$

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. - $\mathrm { k } = 1 ; \mathrm { f } ( \mathrm { x } ) = 5 \mathrm { x } ^ { 3 } + 7 \mathrm { x } ^ { 2 } + 4 \mathrm { x } + 6$ ; Upper bound?

Divide using synthetic division, and write a summary statement in fraction form. - $\frac { 2 x ^ { 3 } + 3 x ^ { 2 } + 4 x - 10 } { x + 1 }$

Solve the problem. -In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $x$ : $y = \frac { 0.53 x } { 100.5 - x }$ . How many hours of study are needed to score 89 ?

Write an equation for the linear function f satisfying the given conditions. - $f ( - 3 ) = 4$ and $f ( 1 ) = 1$

Use the Rational Zeros Theorem to write a list of all potential rational zeros - $f ( x ) = 26 x ^ { 3 } + 104 x ^ { 2 } + 2 x - 13$

Match the equation to the correct graph. - $y = 2 ( x - 2 ) ^ { 2 } - 4$

Write the polynomial in standard form and identify the zeros of the function. - $f ( x ) = x ( x + 3 ) ( x + 2 - i ) ( x + 2 + i )$

Evaluate the limit based on the graph of f shown. - $\lim _ { x \rightarrow 2 ^ { - } } f ( x )$

Match the equation to the correct graph. - $f ( x ) = - 1 - 2 ( x + 1 ) ^ { 2 }$