Exam 4: Exponential and Logarithmic Functions

Use a graphing device to graph the polynomial $y = 3 x ^ { 4 } - 1$ and describe its end behavior.

Use a graphing device to graph the polynomial $P ( x ) = 3 x ^ { 4 } - 4 x ^ { 3 } - 10 x$ and describe its end behavior.

Find a polynomial of degree 3 with constant coefficient $- 18$ and zeros $- 1$ , $- 2$ , and $3$

Find all horizontal and vertical asymptotes of the function $y( x ) = \frac { 5 } { x - 5 }$

What is the remainder when the polynomial $p ( x ) = 7 x ^ { 500 } - 43 x ^ { 56 } - 3 x ^ { 4 } - 1$ is divided by $( x + 1 )$ ?

Sketch the graph of the function $P ( x ) = ( x - 1 ) ^ { 4 } + 16$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$

Evaluate the expression and write in the form $a + b i$ . $i ^ { 55 }$

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. $y = \frac { 2 x + 4 } { x - 2 }$

Use the Factor Theorem to show that $( x + 2 )$ is a factor of the polynomial. $P ( x ) = x ^ { 5 } + 2 x ^ { 4 } - 13 x ^ { 3 } - 14 x ^ { 2 } + 24 x$

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function, $R ( x ) = 80 x - 0.2 x ^ { 2 }$ where the revenue $R ( x )$ Is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?

Evaluate the expression and write the result in the form a + bi. $3 i \left( \frac { 1 } { 3 } - i \right)$

Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$ And $2$ , with $2$ A double zero

Evaluate the expression $( 1 + i ) ^ { 2 }$ and write in the form $a + b i$

Use a graphing calculator to find all real solutions of the equation. $x ^ { 5 } = x + 3$

Which of the following is a factor of the polynomial? $P ( x ) = x ^ { 5 } + 2 x ^ { 4 } - 13 x ^ { 3 } - 14 x ^ { 2 } + 24 x$

Find all vertical asymptotes of the function $y ( x ) = \frac { x - 2 } { x ^ { 2 } - 2 x - 8 }$

Use a graphing calculator to find all real solutions of the equation. $- 3 x = - \frac { 2 } { 3 } - 3 x ^ { 2 }$

Evaluate the expression and write the result in the form a + bi. $\frac { 36 } { 6 - 6 i }$

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 6 } { x - 6 }$ .

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function, $R ( x ) = 40 x - 0.2 x ^ { 2 }$ where the revenue $R ( x )$ is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?