CPhill

These are always a little  difficult

The function (x + 2)^2   is a parabola that opens upward with a vertex of ( -2, 0)

All the graphs show this

The function   l x l  + 1   has a  y value of 

2 at x = -1

1 at x = 0

2 at x  = 1

This eliminates the first three graphs

So....by process of elimination, the last graph  must be the correct one....!!!

Do you see this OK ????

1.  The relative minimum  is the low point on the graph....this is  -36

The relative max  is the high point on the graph....this is 64

2.  f (x) = 8x^2 + 16x  + 6         g (x)  = x^3 - 3x^2  - 9

So   ( f + g) x   =    f (x) + g (x)   =

x^3  + 8x^2 - 3x^2 + 16x + 6  - 9  =

x^3  + 5x^2 + 16x - 3  ......so.....true  !!!

3.  5pi / 3

To convert to  degrees we have

5pi / 3  *    180  / pi  =

5pi / (3 pi) * 180  =

(5/3) * 180  =

5 * (180 / 3)  =

5 * 60  =

300°

The sum is given by

[ distance on day 1 + distance on day 12 ]  *  12  / 2

The distance on day 12 is   

1.5  + .5 (11)   =   7

So...we have

[ 1.5  + 7 ] * 12  / 2  =

[ 8.5 ] * 6  =

51  miles

Your answer is correct....!!!!

Just  enter "6"....then....the multiplication sign, then the square root sign, and then "2"

1.   y= 43(3)^x    would represent the number of pennies after day  x

2. Not sure what this is, but I think we have

f(x)= −0.25(6)^x +2 − 1

The y intercept will be where x  = 0....so we have

-0.25 (6)^{0 + 2}  - 1

-0.25 (6)²  -1

-0.25 (36)  - 1   

-9 - 1  =

-10

3. The practical domain  is  [ 0, 6  ]

Thanks, tertre.....

Here's the "short way"  to find the sum, S₆, at the end of the 6th day....we have that

Sum at any time  =  Initial value  [ 1  - r^n ] / [ 1  - r ]

The initial value is 8

The common ratio, r  = 2

n = the number of days

So we have

S₆  =  8  [ 1 - 2^6]  / [ 1 - 2 ]   =   504  students

Thanks, tertre....If we want  the sum over all 10 weeks........

First week  =  $4

The common difference is 13

Last week  =  4 + 13(9)  =  $121

So....the sum is

[ First week + Last week ]  *   [ Number of weeks  ] / 2  =

[ 4 + 121 ] *  [ 10 ] / 2  =

125  [ 5 ]   =

$625

f(x)  =  x^4  - 9           g (x)  =  x^3 + 9

So....  (f * g) x  =   f(x) * g(x)  =

[ x^4  - 9 }  *  [ x^3 + 9 ]   =

x^7 + 9x^4  - 9x^3  - 81

Note that the first  few terms are

7,  -28,  112, - 448  ......

So....the first term, a₁,   is   7

And the a_n term is  given  by   -4 (a_n-1)

So....the rule is

a_n  = -4 (a _n-1),   a₁  = 7