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I believe the vertical shift is down 5, but I don't know about the horizontal shift.
when does the argument for sin equal zero?
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?
wait, sorry. this lesson confused me a lot. am i supposed to get x alone in 2x+pi=0?
so it would be x= -pi/2 ?
correct so our normal value at x=0, has now been shifted over to x=-pi/2
so the answer would be down 5 and left pi/2?
alright thank you! do you think you could help me with one more problem?
one more, sure, if my sanity holds
tell me your thoughts on how to approach it
i honestly have no idea i'm sorry. please don't lose your sanity lol
what would you say is the value of x for all points on the y axis?
doesn't the x value vary depending on what the y is?
|dw:1433275550605:dw| where do we generally put the y axis? for what value of x does it pass thru?
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)
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?
the y axis usually passes through the 0 on the x axis
got caught in a spin cycle ... but yes, it passes thru where x=0
so, lets compare our functions, when x=0
so for the table, x=0 when y=0?
more appropriately: y=0, when x=0, but yeah
so the y-intercept of the f(x) table is 0?
correct: f(0) = 0 g(0) is what?
would it be -3? i think the number at the end is the y-intercept but i'm not sure
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.
what is the y intercept of: y = 2cos(x) + 1 ??
yep, so "the last term" is not a valid approach is it?
no, i see now though. so the y-intercept of f(x) would be the answer to that one?
0 is more than -2, yes g(0) < f(0) -2 < 0
or -3 depending on what keys we want to hit ...
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!
good luck :)