Exam 3: Polynomial and Rational Functions

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the form f(x) = (x - c)(quotient). - $f ( x ) = 5 x ^ { 4 } - 7 x ^ { 3 } + 17 x ^ { 2 } - 21 x + 6 ; c = 1$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right)$

Find the power function that the graph of f resembles for large values of |x|. - $f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }$

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree 3: zeros: $1 + i$ and $- 9$

Solve the inequality. - $x + \frac { 30 } { x } < 13$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: $- 2,2 + i , - 1 - i , 0$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - $g ( x ) = \frac { 5 x } { ( x + 2 ) ( x + 4 ) }$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - $f ( x ) = \frac { 8 x } { x - 3 }$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 3 x ^ { 5 } - 2 x ^ { 2 } + 6 x - 1$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { 10 x } { x ^ { 2 } - 19 }$

Find the x- and y-intercepts of f. - $f ( x ) = x ^ { 2 } ( x - 1 ) ( x - 5 )$

Find the domain of the rational function. - $f ( x ) = \frac { x ( x - 1 ) } { 16 x ^ { 2 } + 24 x + 5 }$

Determine the maximum number of turning points of f. - $f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -The acceleration due to gravity $g$ (in meters per second per second) at a height h meters above sea level is given by $g ( h ) = \frac { 3.99 \times 10 ^ { 14 } } { \left( 6.374 \times 10 ^ { 6 } + h \right) ^ { 2 } }$ where $6.374 \times 10 ^ { 6 }$ is the radius of Earth in meters. Death Valley in California is $86 \mathrm {~m}$ below sea level. a) Find the value of $g ( h )$ at Death Valley to four decimal places. b) Compare the value in (a) to the value of $g ( h )$ at sea level.

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f ( x ) = ( x + 2 ) ^ { 4 } + 3$

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }$

Use the graph to determine the domain and range of the function. -

Find the x- and y-intercepts of f. - $f ( x ) = 4 x ^ { 2 } ( x + 3 ) ^ { 3 }$

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 4 ; zeros: $1 , - 1$ , and $4 - 2 \mathrm { i }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x - 8 } { x ^ { 2 } + 15 x - 9 }$