Exam 4: Exponential and Logarithmic Functions

Sketch the graph of the function $P ( x ) = ( x - 1 ) ^ { 5 } + 16$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$ ) Indicate all $x$ - and $y -$ Intercepts on your graph

Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4$

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

Evaluate the expression $( 4 - i ) ( 4 + i )$ and write in the form $a + b i$

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } - 256$

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

Find all rational, irrational, and complex zeros (and state their multiplicities). $P ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } + 24 x - 16$

Find all rational, irrational, and complex zeros (and state their multiplicities). $P ( x ) = x ^ { 4 } - 16$

Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$ and $2$ , with $2$ a double zero. (There are many possibilities.)

Find all vertical asymptotes of the function $y ( x ) = \frac { x - 5 } { x ^ { 2 } - 5 x + 4 }$

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

Divide. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$