Exam 3: Polynomial and Rational Functions

Use the graph to determine the domain and range of the function. - A) domain: $\{ x \mid x > 0 \}$ range: $\{ y \mid y \neq 4 \}$ B) domain: $\{ x \mid x \neq 4 \}$ range: $\{ y \mid y > 0 \}$ C) domain: $\{ x \mid x \neq 4 \}$ range: $\{ y \mid y \geq 0 \}$ D) domain: $\{ x \mid x \geq 0 \}$ range: $\{ y \mid y \neq 4 \}$

Find the domain of the rational function. - $g ( x ) = \frac { x } { x ^ { 3 } - 216 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)$

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. - $x ^ { 3 } - 8 x - 3 = 0 ; - 3 \leq x \leq - 2$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 } { x ^ { 2 } + 9 x + 8 }$

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = x ^ { 4 } + 25 x ^ { 2 } + 144$

Find the domain of the rational function. - $f ( x ) = \frac { 5 x } { ( x - 6 ) ( x + 8 ) }$

Use the given zero to find the remaining zeros of the function. - $f ( x ) = 2 x ^ { 4 } - 17 x ^ { 3 } + 71 x ^ { 2 } - 153 x + 117 ; \text { zero: } 2 + 3 i$

Use the graph to find the vertical asymptotes, if any, of the function. - A) $x = - 4 , x = 4 , x = 0 , y = 1$ B) $x = - 4 , x = 4 , x = 0$ C) $x = - 4 , x = 4$ D) $x = - 4 , x = 4 , y = 1$

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

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have. - $f ( x ) = x ^ { 2 } - 18$

Solve the inequality. - $\frac { x ^ { 2 } ( x - 11 ) ( x + 2 ) } { ( x - 4 ) ( x + 8 ) } \geq 0$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \frac { 2 - x ^ { 4 } } { 9 }$

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

Solve the problem. - $( a + 4 ) ( a - 4 ) ( a - 5 ) > 0$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { 2 x ^ { 3 } + 11 x ^ { 2 } + 5 x - 1 } { x ^ { 2 } + 6 x + 5 }$

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have. - $f ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + x + 4$

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

Solve the problem. -The profits (in millions) for a company for 8 years was as follows: Year, x Profits 1993,1 1.1 1994,2 1.7 1995,3 2.0 1996,4 1.4 1997,5 1.3 1998,6 1.5 1999,7 1.8 2000,8 2.1 Find the cubic function of best fit to the data.

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