In what direction and by how many units is the graph of f(x) = 6 sin(2x + π) − 5 vertically and horizontally shifted?

- anonymous

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- anonymous

I believe the vertical shift is down 5, but I don't know about the horizontal shift.

- amistre64

when does the argument for sin equal zero?

- amistre64

in other words
y = sin(x) is the parent function
its 'center' is defined when x=0
to know how for it shifts on the x axis, the argument of x gets adjusted to read:
2x+pi
so when does 2x+pi = 0?

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- anonymous

wait, sorry. this lesson confused me a lot. am i supposed to get x alone in 2x+pi=0?

- amistre64

yes

- anonymous

so it would be x= -pi/2 ?

- amistre64

correct
so our normal value at x=0, has now been shifted over to x=-pi/2

- anonymous

so the answer would be down 5 and left pi/2?

- amistre64

yep

- anonymous

alright thank you! do you think you could help me with one more problem?

- amistre64

one more, sure, if my sanity holds

- anonymous

Which of the following functions has the greatest y-intercept?

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- amistre64

tell me your thoughts on how to approach it

- anonymous

i honestly have no idea i'm sorry. please don't lose your sanity lol

- amistre64

what would you say is the value of x for all points on the y axis?

- anonymous

doesn't the x value vary depending on what the y is?

- amistre64

|dw:1433275550605:dw|
where do we generally put the y axis? for what value of x does it pass thru?

- amistre64

do not confuse a function, for how we measure the function.
the function is a curve, for a given value of x, we can measure how far the curve is from the x axis, by comparing it against the y axis.
say we have a function that measures the height of a tree at a given day.
the tree is the object that we are measuring (it is the function)
the height of the tree is NOT the function, it is how we are measuring it. (the y axis)

- amistre64

if we want to know WHERE the function intersects (crosses over or hits) the y axis ... we should be cognizant of where the y axis is to start with. right?

- anonymous

the y axis usually passes through the 0 on the x axis

- amistre64

got caught in a spin cycle ... but yes, it passes thru where x=0

- amistre64

so, lets compare our functions, when x=0

- amistre64

|dw:1433276240758:dw|

- anonymous

so for the table, x=0 when y=0?

- amistre64

more appropriately: y=0, when x=0, but yeah

- anonymous

so the y-intercept of the f(x) table is 0?

- amistre64

correct: f(0) = 0
g(0) is what?

- anonymous

would it be -3? i think the number at the end is the y-intercept but i'm not sure

- amistre64

its not the number on the end, is the value when x=0
which in this particular case
g = 4 sin(4x) - 3
g = 4 sin(0) - 3
g = 0 - 3
is -3, but dont go by "last term", its not a good conjecture.

- amistre64

what is the y intercept of:
y = 2cos(x) + 1 ??

- anonymous

3?

- amistre64

yep, so "the last term" is not a valid approach is it?

- anonymous

no, i see now though. so the y-intercept of f(x) would be the answer to that one?

- amistre64

0 is more than -2, yes
g(0) < f(0)
-2 < 0

- amistre64

or -3 depending on what keys we want to hit ...

- anonymous

haha i understood it! thanks a lot for your help. i'm not too great with math but you were really patient so thank you!

- amistre64

good luck :)

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