Exam 3: Polynomial and Rational Functions

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 4 x ^ { 3 } + 19 x ^ { 2 } - 8 x + 15$

Find the x- and y-intercepts of f. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 9 \right)$

Find a bound on the real zeros of the polynomial function. - $f ( x ) = x ^ { 5 } + 3 x ^ { 4 } + 5 x ^ { 3 } - 2 x ^ { 2 } + 4 x - 1$

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function. - $f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 4$ A) B) C) D)

Solve the inequality. - $\frac { 14 } { x - 6 } > \frac { 12 } { x - 1 }$

Find the x- and y-intercepts of f. -f(x) = (x - 2)(x - 6)

Solve the problem. -The distance formula states that d = rt. If a car drives 50 miles, the function r $r = \frac { 50 } { t }$ is a rational function. Find the asymptotes of this function.

Graph the function. - $f(x)=\frac{2 x}{(x+3)(x-1)}$ A) B) C) D)

Find the indicated intercept(s) of the graph of the function.2133:2139 - $x \text {-intercepts of } f ( x ) = \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 7 x - 9 }$

Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of | $| x |$ (b) Find the x- and y-intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Graph f using a graphing utility. (e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing. - $f ( x ) = x ^ { 2 } ( x + 3 )$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y \text {-intercept of } f ( x ) = x + \frac { 25 } { x }$

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

Use the graph to find the oblique asymptote, if any, of the function. -

Graph the function. - $f ( x ) = \frac { x } { x ^ { 2 } - 9 }$ A) B) C) D)

Find the x- and y-intercepts of f. - $f ( x ) = 2 x ^ { 4 } ( x - 1 ) ^ { 3 }$

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

Solve the equation in the real number system. - $x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - x - 10 = 0$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = - 14 x ^ { 3 } + 9 x ^ { 2 } - 7$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { 23 } { ( x + 10 ) \left( x ^ { 2 } - 5 \right) }$

Graph the function using transformations. - $f ( x ) = \frac { 2 } { ( 3 + x ) ^ { 2 } }$ A) B) C) D)