Exam 3: Polynomial and Rational Functions

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

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; x - 14$

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

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: -3, -2, 3; degree 3 A) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 9 x + 18$ B) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18$ C) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18$ D) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 9 x + 18$

Use the graph to determine the domain and range of the function. - A) domain: $\{ x \mid x \neq 0 \}$ range: $\{ y \mid y \leq - 6$ or $y \geq 6 \}$ B) domain: all real numbers range: $\{ y \mid y \leq - 6$ or $y \geq 6 \}$ C) domain: $\{ x \mid x \leq - 6$ or $x \geq 6 \}$ range: $\{ \mathrm { y } \mid \mathrm { y } \neq 0 \}$ D) domain: $\{ x \mid x \neq 0 \}$ range: all real numbers

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

Solve the problem. - $x ^ { 2 } + 6 x \leq 0$

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: -5, multiplicity 2; -1, multiplicity 1; degree 3 A) $x ^ { 3 } + 11 x ^ { 2 } + 35 x + 25$ B) $x ^ { 3 } - 11 x ^ { 2 } + 10 x - 25$ C) $x ^ { 3 } + 10 x ^ { 2 } + 35 x + 25$ D) $x ^ { 3 } - 11 x ^ { 2 } + 35 x - 25$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 4; zeros: $5 - 5 \mathrm { i }$ , $8 \mathrm { i }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { ( x - 6 ) ^ { 2 } } { ( x + 11 ) ^ { 3 } }$

Solve the problem. - $x ^ { 2 } - 8 x + 7 > 0$

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

Solve the inequality. - $\frac { 3 x } { 7 - x } < x$

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. - $f ( x ) = x ^ { 3 } - 0.4 x ^ { 2 } - 2.5861 x + 3.0912$

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

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. - $f ( x ) = 5 x ^ { 3 } - 2 x ^ { 2 } + 25 x - 10$

Solve the problem. -A lens can be used to create an image of an object on the opposite side of the lens, such as the image created on a movie screen. Every lens has a measurement called its focal length, f. The distance s1 of the object to the lens is related to the distance $\text { s2 }$ of the lens to the image by the function $\mathrm { s } _ { 1 } = \frac { \mathrm { fs } _ { 2 } } { \mathrm {~s} _ { 2 } - \mathrm { f } }$ For a lens with f = 0.3 m, what are the asymptotes of this function?

Solve the problem. -For what positive numbers will the cube of a number exceed 9 times its square? A) $\{ x \mid x > 9 \}$ B) $x |0 < x < 81 \}$ C) $x |0 < x < 9 \}$ D) $x \mid x > 81 \}$

Use the graph to find the vertical asymptotes, if any, of the function. -

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