CPhill

Exponential

See the graph of  y  = 2^x   :  https://www.desmos.com/calculator/btsykhud9v

End Behavior...at the left end, the graph approaches  y  = 0   ...at the right end it approaches  infinity  = "up"

Avg Rate of Change ;: Calculius again....there is no average rate of change....th slope at any x value  is   2^x * ln (2)

Positve/ Negative :  The graph is positive for all x...the range is  (0, inf )

x , y intercepts  -  no x intercept...y intercept is  (0,1).... [which is true for all graphs of the form  y  =  a^x]

Real world :  Used to model growth rates in populations, etc.

Log

See the graph of  y  = log (x)  here   : https://www.desmos.com/calculator/nxcaogf186

End Behavior :  Near x  = 0, the graph turns downward.....as the graph increases from left to right, its end behavior  is "up" on the right

Avg Rate of Change....there is no "Average rate of change"...again Calculus will show that the slope at any point x  is :

1 / [x ln 10 ]

Positive/ Negative  :  the graph is  negative  [ below the x axis} on  (0, 1)....the graph is above the x axis on (1, inf)

x, y intercept :   this graph never intercepts y, because we can't take the log log of  x  = 0.....the x intercpt  is at  x  = 1

Real World :  logs are used in  the calculation of magnitudes of earthquakes

Area to  be covered  x  [  qts / area ]

[ 241  + 59  ]  x   [ 2  / 200 ]  = 

[ 300]  x [ 1 / 100] =

300 / 100  =

3 quarts

Square root

See the graph of  y  = https://www.desmos.com/calculator/cooqsnkeug

End behavior.....this graph  always rises from left to right on its domain.....so..."Up"  on the right

Average Rate of  Change :  THere is no "average rate of change"...again....this requires Calculus...the "average rate of change "  is the slope at any point on the graph  [except x =   0 ] and is  given by   (1/2) x ^(-1/2)...at  x = 0  th slope is undefined

Positive/Negative :  The graph has a range  of  [0, infinity)  it is never negative

x / y intercept  = (0,0)

Again....I can't name any real world applications off the top of my head....(sorry !! )

Second one

The graph is  of  y  = l x l  .....https://www.desmos.com/calculator/wn5b3geed5

End behavior : Up at both ends

Average rate of change :  on (-inf, 0)  the average rate of change  = -1....on (0, inf), the average rate of change is 1

Positiive / Negative  -  the graph is never negative...thae range  is [ 0, inf )

X, y intercept  = (0,0)

How used in the real world : Can't think of any....but I'm sure there are some  !!!

Well..I'll see what  I can do....but...I can't promise that I can get to each one!!!

First one

Th quadratic is  y  = x^2   [a parabola ]

Here's the graph : https://www.desmos.com/calculator/3gdzi6zvsn

End Behavior :  Up  at both ends

Average Rate of Change  [ I don't see how your teacher expects you to know this ... you need Calculus]....there is  no "average rate of change"....the rate of change [slope of the graph ]  at any value of x  = 2x

Positve/Negative  ..I assume this refers to the range ??...The graph is never negative  for  y...in other words, the range is  [0, infinity )

x intercept  and y intercept  =  (0,0)

How used in the real world.....If you have a sattelite dish....it is a parabola....the satellite beams the signal to the dish...it is reflected back to the focus of the parabola and transmitted to your inside receiver 

Good job, tertre  !!!

No ordered pairs shown....but...no prob

x+5y = −15   

 y =  1/5x+1

Rearrange the first as  x  = -15  - 5y

Sub this into the second for  x

y  =  (1/5)(-15 - 5y) + 1  simplify

y = -3 - y + 1    add y to both sides

2y  =  -3 + 1

2y = -2    divide both sids by 2

y  = -1

So

x  = -15 - 5(-1)  =  -15 + 5  =   -10

So   (x, y)  = ( -10, -1)

That's a lot to chew on  at one time....when do you need this by  ??

Last one....this is the most difficult

We have a trapezoidal prism

The area of the two trapezoids forming the sides  = 

2 * (1/2) (height) ( sum of the base lengths )  =

2 *(1/2) (7.8) ( 17 + 8 )    =  195 m^2

We have two other congruent sides that are rectangles  with height  = 9m  and width  = 8 m

So..their combined area  =  2 * 9 * 8    = 144 m^2

And the top is a rectangle  with dimensions of  8 and 17

So its area is  8 * 17  = 136m^2

And the bottom is a square with a side of  8  ...so its area  = 8^2  = 64 m^2

So...the total surface area  is  195  + 144 + 136 + 64  = 539  m^2