Algebra 2 - Rational Functions and Sequence & Series

Select the function that is NOT a rational function.

•  $y=\frac{3x^2}{x-2}$  

•  $y=7x-5$  

•  $y=\sqrt{x+4}$  

•  $y=\frac{x-2}{2x+8}$  

Select each sequence that is a geometric sequence.

•  $5,\ 10,\ 20,\ 40,\ 80,\ .\ .\ .\$  

•  $-3,\ 1,\ 5,\ 9,\ 13,\ .\ .\ .\$  

•  $8,\ \frac{16}{3},\ \frac{32}{9},\ \frac{64}{27},\ \frac{128}{81},\ .\ .\ .\$  

•  $2,\ 2k,\ 2k^2,\ 2k^3,\ 2k^4,\ .\ .\ .\ \ \ k\ne0,\ k\ne1$  

•  $4,\ 20,\ 120,\ 840,\ 6720,\ .\ .\ .\$  

Explain, in your own words, how to determine if a sequence is arithmetic or not.

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What are the next 3 terms in the sequence?

 $5,\ 15,\ 25,\ 35,\ ?\ ,\ ?,\ ?$  

•  $55,\ 65,\ 75$  

•  $45,\ 55,\ 65$  

•  $40,\ 45,\ 50$  

•  $70,\ 140,\ 280$  

Which rational function has a hole in the graph?

• $y=\frac{x}{x+5}$

• $y=\frac{x-2}{x\left(x-3\right)}$

• $y=\frac{x+1}{\left(x+1\right)\left(x-5\right)}$

• $y=\frac{x+3}{\left(x+1\right)\left(x-2\right)}$

 $4,\ 12,\ 36,\ 108,\ .\ .\ .\$  State the common ratio of the geometric sequence . . .

Write your answer as a single number; Example Response: 7

What is the recursive formula for the given sequence?

 $2,\ 10,\ 50,\ 250,\ .\ .\ .\$  

•  $a_1=2;\ \ a_n=5\cdot a_{\left(n-1\right)}$  

•  $a_n=5\cdot a_{\left(n-1\right)}$  

•  $a_n=2\cdot5^{\left(n-1\right)}$  

•  $a_1=2;\ \ a_n=a_{\left(n-1\right)}+5$  

Which of the following is the sum of the first 20 terms of this arithmetic sequence?
 $1,\ 5,\ 9,\ 13,\ 17,\ .\ .\ .\$  
Recall:  

 $s_n=\frac{n}{2}\left(a_1+a_n\right)$   and  $a_n=a_1+\left(n-1\right)\cdot d$  

• 78

• 780

• 77

• 1560

Which of the following is the proper set up to find the sum of the first 15 terms of the geometric sequence?
 $12,\ 9,\ \frac{27}{4},\frac{81}{16},\frac{243}{64},\ .\ .\ .\$  

•  $a_{15}=12\cdot\left(\frac{3}{4}\right)^{14}$  

•  $s_{15}=\frac{15\left(1-\left(\frac{3}{4}\right)^n\right)}{1-\frac{3}{4}}$  

•  $s_{15}=\frac{12\left(1-\left(\frac{1}{4}\right)^n\right)}{1-\frac{1}{4}}$  

•  $s_{15}=\frac{12\left(1-\left(\frac{3}{4}\right)^n\right)}{1-\frac{3}{4}}$  

What is the vertical asymptote for the graph of the following rational function?

 $y=\frac{x+4}{x-3}$  

•  $x=-4$  

•  $x=-3$  

•  $x=3$  

•  $y=3$