Exam 3: Polynomial and Rational Functions

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

Solve the equation in the real number system. - $3 x ^ { 3 } - 14 x ^ { 2 } + 13 x + 6 = 0$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { 6 x ^ { 3 } + 22 x ^ { 2 } + 35 x + 31 } { 3 x + 5 }$

Find the vertical asymptotes of the rational function. - $g ( x ) = \frac { x } { x ^ { 3 } - 343 }$

Solve the inequality. - $x ( x + 3 ) ( 5 - x ) \geq 0$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x ^ { 3 } - 27 } { x ^ { 2 } - 25 }$

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 4 ; zeros: $2 \mathrm { i }$ and $- 5 \mathrm { i }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = x ( x - 9 )$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 4 x + 6$

Solve the inequality. - $( x - 1 ) \left( x ^ { 2 } + x + 1 \right) >$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { ( 5 x - 15 ) ( x - 4 ) } { x ^ { 2 } + 12 x - 19 }$

Write the word or phrase that best completes each statement or answers the question. 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. - $f ( x ) = x ^ { 2 } ( x + 3 )$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - $R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 4 x - 12 }$

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

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 3 ; zeros: 4,1 - i

Find the x- and y-intercepts of f. - $f ( x ) = 5 x - x ^ { 3 }$

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

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = x + \frac { 1 } { x }$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 } { x ^ { 2 } + 9 x + 8 }$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { 5 } { x ^ { 2 } - x - 12 }$