CPhill

y= (3x^3) - x - 3    

The end behavior will be towards -infinity as x approaches some large negative value and towards + infinty as x approaches some large positve value

The maximum number of turning points will be two and the minimum number willl be zero......

We could find the potential turning points using Calculus, but.....since you haven't had Calculus, it might be best to look at the graph, here:   https://www.desmos.com/calculator/kjh6bkkj2b

There are two turning points...one at (-1/3 , ≈ -2.778)  and the other at (1/3, ≈ -3.222)

Let N be the first integer and N + 1the second...and we have

N + (N + 1)    = 153 simplify

2N + 1  = 153     subtract 1 from both sides

2N  = 152    divide both sides by 2

N  = 76

And N + 1  = 77

Post your problems.....

2x^2 + 32x - 114 = 0    divide through by 2

x^2 + 16x - 57   =  0    factor

(x + 19) ( x - 3)   = 0

Setting both factors to 0 we have that x  = -19  or  x  = 3

Measure of any interior angle of a regular polygon  =  (n - 2)* 180 / n      where  n is the number of sides 

Measure of an exterior angle  = 360/ n

Sum of all interior angles  =   (n - 2)(180)

9 x^ 2 + 25 y^ 2 =225    divide both sides by 225  to put the equation of the ellipse in standard form

x^2/ a^2  + y^2/ b^2  = 1   

x^2 / 25  + y^2 / 9    =   1

The major axis lies along the x axis  and is 2a units in length   and "a" can be found as follows......√a^2  = √25  →   a  = 5

So....2a  = 2 (5)   = 10  units  = 10 yards  = 30 feet =  the length of the major axis

first....factor each number into primes

4 = 2^2

8 = 2^3

10  = 2 * 5

To find the LCM....take the product of each unique factor along with its highest represented power...so we have

2^3  * 5    =

8 * 5   =

40

 [ √2 + √8  ]   /  [ √5   - √8]      multiply top/bottom by  √5   + √8   

[ √2 + √8] [ √5   +  √8]  /  [  5 - 8 ]  =

[ √10 + √40 + √16 + √ 64 ]  / -3  =

[ √10 + 2√10 + 4 + 8 ]  / -3  =

[ 12 + 3√10 ] / -3  =

3 [ 4 + √10 ] / -3

-1 [ 4 + √10 ]

-4 - √10

The lenngth of the major axis / 2  = a = 10     ...the length of the minor axis/ 2  = b  = 7

The focal length, c, is given by : √[ a^2 - b^2 ] = √[ 10^2 - 7^2 ]  = √51 units......and the distance between the focal points  = 2c  = 2√51 ≈ 14.28  units 

"D"   is correct... in a function, if we have a  finite number of values in the domain....each of these will be paired with some y value....

"A" has a finite domain, but not an  "infinite" cost   [ infinite range]....the cost depends upon the number of minutes but it is never greater than 100m ....where m represents the cost per minute

"B"   has some finite domain domain .....  but also a finite range of $100

"C"  has some finite domain and range  [ we assume that there are not an infinite number of minutes in each billing cycle....!!!!!]