Question

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

Answer 1

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

Answer 2

when does the argument for sin equal zero?

Answer 3

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?

Answer 4

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

Answer 5

yes

Answer 6

so it would be x= -pi/2 ?

Answer 7

correct

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

Answer 8

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

Answer 9

yep

Answer 10

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

Answer 11

one more, sure, if my sanity holds

Answer 12

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

Answer 13

tell me your thoughts on how to approach it

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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)

Answer 19

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?

Answer 20

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

Answer 21

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

Answer 22

so, lets compare our functions, when x=0

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

correct: f(0) = 0

g(0) is what?

Answer 27

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

Answer 28

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.

Answer 29

what is the y intercept of:

y = 2cos(x) + 1 ??

Answer 30

3?

Answer 31

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

Answer 32

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

Answer 33

0 is more than -2, yes

g(0) < f(0)

-2 < 0

Answer 34

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

Answer 35

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!

Answer 36

good luck :)