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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)
what's the parent function of g(x) = log (x + 4)
let me graph it on my calc

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(0, 0.60)
when I say "parent" function, I'm talking about the most basic form of it before you do any transformations
example: x^2 is a parent function (x+2)^2 + 7 is a transformed version of the x^2 parent function
idk
here's a list of parent functions commonly used http://www.toomey.org/tutor/harolds_cheat_sheets/Harolds_Parent_Functions_Cheat_Sheet_2014.pdf
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
oh okay so it would be a natural log
or just log
k
I would say that log(x) is the parent of log (x + 4)
that would be the answer for 1?
how would you describe the transformation?
like how it would look on a graph?
yeah if you want, you can compare the parent function y = log(x) to y = log(x+4)
how are those two different? how are they similar?
they both start from a negative y and go up to a positive y moving to a greater number of x value?
|dw:1443229687081:dw|
|dw:1443229706167:dw|
they have the same basic curve shape, yes
like that
the only difference is that log(x+4) is shifted 4 units to the left. You have the correct graphs
you'll follow these same steps for 2 through 4
oay cool i thin i got it can i try doing number 2 by my self
go for it
so number 2 in would be shifter 3 units down and fliped upside down
you actually flip first, then shift 3 units down
the order matters (if you want, cut out a parabolic shape on paper, and play around with the 2 orders)
parent: x^2 flip over x axis: x^2 -----> -x^2 shift down 3 units: -x^2 -----> -x^2 - 3
oh ok
3 would go from this |dw:1443230322910:dw| to this
|dw:1443230407412:dw|
3 is this right? \[\Large \frac{2}{x+5}\]
yup
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
what is the parent function here
1/x
when we go to 2/x, what happens to the graph?
the ones in the negative x valuves move 2 unites to the left and vice versa
how are you graphing these functions? on paper? or with a graphing calculator?
calc
oh and it will also move down
I'm using desmos if you want to use that here's the link https://www.desmos.com/calculator
here are 1/x and 2/x plotted together https://www.desmos.com/calculator/mgo61oouia
what differences do you see?
it moves half a unit
well stretching is being done here. Vertical stretching by a factor of 2
eg: (1,1) on 1/x turns into (1,2) on 2/x
then notice how the green graph is shifted 5 units to the left to get 2/(x+5) https://www.desmos.com/calculator/ul6qdzno6d
oh okay i see
for the last one would it ve a vertical flip and shifts 4 units to he right
no, that would be true if it were e^(x-4)
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
if in doubt, graph to check
oh ookkk
than you so much
np

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