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# Parent graphs

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12 Do you ever understand something but not understand it at the same time? That's where I'm at right now.

Aug 29, 2018

#1
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That's a lot to chew on  at one time....when do you need this by  ??   Aug 29, 2018
#2
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Tomorrow lol

RainbowPanda  Aug 29, 2018
#3
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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   Aug 29, 2018
edited by CPhill  Aug 29, 2018
#4
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You are a freaking lifesaver, I love you xD

Thank you so much!

RainbowPanda  Aug 29, 2018
#5
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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  !!!   Aug 29, 2018
#6
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Yeah I got one for real world, thanks ^-^

RainbowPanda  Aug 29, 2018
#7
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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 !! )   Aug 29, 2018
#8
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It's alright I can think of some real world problems ^-^

RainbowPanda  Aug 29, 2018
#9
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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   Aug 29, 2018
#10
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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.   Aug 29, 2018
#11
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Last One  [ you owe me  BIG TIME...LOL!!! ]

Rational

These might be anything but here is the graph of   y  = (x + 1)  /( x - 1)  :  https://www.desmos.com/calculator/watidrudhk

[ This is actually the graph of a "rotated" hyperbola ]

End Behavior : Far left end : UP   ...as we approach x = 1 from  the  left :  DOWN....as we approach x = 1 from the right : UP.....as we approach infinity : DOWN

Avg Rate of Change...Calculus, again...there is no "average rate of change"...the slope at any point on the graph is :

-2/ (x -1)^2

Positive/ Negative : The graph is  above the x axis  on  (-inf, -1) U ( 1, inf)..it is below the x axis on ( -1, 1)

x, y intercepts  :  intercepts x axis at  (-1,0)  and the y axis  at (0, -1)

Real World :  If you find any, let me know  !!!  LOL!!!   Aug 29, 2018
#12
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Oh my goodness, I don't know how I could ever repay you!! <3

RainbowPanda  Aug 29, 2018