Review for Functions, Part 1 Quiz 2

• $f\left(n\right)\ =\ 12n\ -\ 6$
  

• $f\left(n\right)\ =\ 9n\ +\ 6$

• $f\left(n\right)\ =\ 9n\ -\ 3$

• $f\left(n\right)\ =\ 3n\ +\ 3$

Answer explanation

If you use the sequence formula $f\left(n\right)\ \left[or\ \ a\left(n\right)\right]\ =\ d\left(n-1\right)\ +\ f\left(1\right)\ \left[or\ \ a\left(1\right)\right]$ and then plug in the information in the table (d=9, and a(1) = 6, you get f(n) = 9(n-1) + 6. Distribute the 9 and then simplify to get the correct equation.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Which statement(s) is (are) true?

Select ALL that apply.

• The linear function has a maximum value at (3,10)

• The linear function has a minimum value at (-10,-3)

• The linear function has an x-intercept at (-7,0)

• The linear function has a y-intercept at (0,7)

• The linear function has a y-intercept at (0,-7)

What is the domain of the function and the best description of the x values?

• $x\ge0$ , where x is an integer.

• $x\ge0$ , where x is rational.

• $0\le x\le100$ , where x is an integer.

• $0\le x\le100$ , where x is rational.

Which function defines the terms in Mr. Smith's sequence, where  $a_n$  is the nth term of the sequence?

•  $a\left(n\right)\ =\ \frac{5}{2}\ +\ 8n$  

•  $a\left(n\right)\ =\ \frac{11}{2}\ +\ 8n$  

•  $a\left(n\right)\ =\ \frac{5}{2}\ +\ 8\left(n\ -1\right)$  

•  $a\left(n\right)\ =\ \frac{11}{2}\ +\ 8\left(n-1\right)$  

Answer explanation

Be sure you know what the equivalent improper fraction is for  $5\ \frac{1}{2}$  .

Tags

CCSS.HSF.BF.A.2

For which intervals is the function constant?

Hint: constant = not changing (slope that is)

• $0<x<2\ and\ 5<x<7$

• $2<x<4\ and\ 5<x<7$

• $2<x<4\ and\ 8<x<10$

• $4<x<5\ and\ 7<x<8$

Write a function  $\left[c\left(n\right)\right]$  to represent the cost of ice cream, c, with n number of toppings. 

Hint: the "template in function notation" for an arithmetic sequence is  $a\left(n\right)=d\left(n-1\right)\ +\ a\left(1\right)$  , so determine your common difference and your first term and plug those in, distribute and simplify to write the function.

Tags

CCSS.HSF.BF.A.2

What's a reasonable domain for this function?

• all real numbers

• only positive integers including zero

• only whole numbers

• all positive real numbers including zero

What is the recursive formula for this arithmetic sequence?

The "template" for the recursive formula is  $a_1\ =\left(first\ term\ in\ sequence\right)\ and\ a_n\ =\ \left(n\ -1\right)\ +\ d$  

• 
  

   $a_1=12$   $a_n=n\ -\ 6$  
  

•  $a_1\ =\ 12$   $a_n\ =\ n\ +\ 4$  

•  $a_1=12$   $a_n\ =\ n\ +\ 6$  

•  $a_1\ =\ 17$   $a_n\ =\ n\ -\ 6$  

Tags

CCSS.HSF.BF.A.2

What is the explicit formula for this arithmetic sequence - 

12,7,2,-3, ...

Hint: the "template for the explicit formula" is  $a_n\ =\ d\left(n\ -\ 1\right)\ +\ a_1$  where d = common difference and  $a_1$  = first term. Plug in what you know, distribute, and simplify.

•  $a_n\ =\ 5n\ +\ 7$  

•  $a_n\ =\ -5n\ +\ 17$  

•  $a_n\ =\ -5n\ +\ 7$  

•  $a_n\ =\ 5n\ -\ 17$  

Tags

CCSS.HSF.BF.A.2

Using this equation $a_n\ =\ -5n\ +\ 17$  , find the 20th term in the sequence 12, 7, 2, -3, ...

• 117

• 83

• -83

• -117

Tags

CCSS.HSF.BF.A.2