@jim_thompson5910

- anonymous

@jim_thompson5910

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- anonymous

DESCRIBE EACH FUNCTION AS ONE OR MORE TRANSFORMATIONS OF IT'S PARENT FUNCTION
1. g(x) = log (x + 4)
2. g(x) = -x^2 - 3
3. g(x) = (2 / x +5)
4. g(x) = e ^(-4x)

- jim_thompson5910

what's the parent function of g(x) = log (x + 4)

- anonymous

let me graph it on my calc

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## More answers

- anonymous

(0, 0.60)

- jim_thompson5910

when I say "parent" function, I'm talking about the most basic form of it before you do any transformations

- jim_thompson5910

example: x^2 is a parent function
(x+2)^2 + 7 is a transformed version of the x^2 parent function

- anonymous

idk

- jim_thompson5910

here's a list of parent functions commonly used
http://www.toomey.org/tutor/harolds_cheat_sheets/Harolds_Parent_Functions_Cheat_Sheet_2014.pdf

- jim_thompson5910

they consist of the basic shapes you'll see in graphs
example: x^2 has a bowl shape. Any other bowl shape graph is most likely based off the parent function of x^2

- anonymous

oh okay so it would be a natural log

- jim_thompson5910

or just log

- anonymous

k

- jim_thompson5910

I would say that log(x) is the parent of log (x + 4)

- anonymous

that would be the answer for 1?

- jim_thompson5910

how would you describe the transformation?

- anonymous

like how it would look on a graph?

- jim_thompson5910

yeah if you want, you can compare the parent function y = log(x) to y = log(x+4)

- jim_thompson5910

how are those two different? how are they similar?

- anonymous

they both start from a negative y and go up to a positive y moving to a greater number of x value?

- anonymous

|dw:1443229687081:dw|

- anonymous

|dw:1443229706167:dw|

- jim_thompson5910

they have the same basic curve shape, yes

- anonymous

like that

- jim_thompson5910

the only difference is that log(x+4) is shifted 4 units to the left. You have the correct graphs

- jim_thompson5910

you'll follow these same steps for 2 through 4

- anonymous

oay cool i thin i got it can i try doing number 2 by my self

- jim_thompson5910

go for it

- anonymous

so number 2 in would be shifter 3 units down and fliped upside down

- jim_thompson5910

you actually flip first, then shift 3 units down

- jim_thompson5910

the order matters (if you want, cut out a parabolic shape on paper, and play around with the 2 orders)

- jim_thompson5910

parent: x^2
flip over x axis: x^2 -----> -x^2
shift down 3 units: -x^2 -----> -x^2 - 3

- anonymous

oh ok

- anonymous

3 would go from this |dw:1443230322910:dw|
to this

- anonymous

|dw:1443230407412:dw|

- jim_thompson5910

3 is this right?
\[\Large \frac{2}{x+5}\]

- anonymous

yup

- anonymous

would it be the one of the negative x values shifted 5 units up and the one in the positive value shifted 5 units down

- jim_thompson5910

what is the parent function here

- anonymous

1/x

- jim_thompson5910

when we go to 2/x, what happens to the graph?

- anonymous

the ones in the negative x valuves move 2 unites to the left and vice versa

- jim_thompson5910

how are you graphing these functions? on paper? or with a graphing calculator?

- anonymous

calc

- anonymous

oh and it will also move down

- jim_thompson5910

I'm using desmos if you want to use that
here's the link
https://www.desmos.com/calculator

- jim_thompson5910

here are 1/x and 2/x plotted together
https://www.desmos.com/calculator/mgo61oouia

- jim_thompson5910

what differences do you see?

- anonymous

it moves half a unit

- jim_thompson5910

well stretching is being done here. Vertical stretching by a factor of 2

- jim_thompson5910

eg: (1,1) on 1/x turns into (1,2) on 2/x

- jim_thompson5910

then notice how the green graph is shifted 5 units to the left to get 2/(x+5)
https://www.desmos.com/calculator/ul6qdzno6d

- anonymous

oh okay i see

- anonymous

for the last one would it ve a vertical flip and shifts 4 units to he right

- jim_thompson5910

no, that would be true if it were e^(x-4)

- jim_thompson5910

we start with e^x which is the parent function
replace the x with -4x. That will do 2 things
a) the negative flips the graph over the y axis
b) the 4 horizontally compresses the graph by a factor of 4
https://www.desmos.com/calculator/5tkhkrwm5e

- jim_thompson5910

if in doubt, graph to check

- anonymous

oh ookkk

- anonymous

than you so much

- jim_thompson5910

np

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