Question

can someone please help me with trig? just two questions

Answer 1

Consider the function y = -2-3cos(x+pi). What effect does the -2 have on the original graph?

Answer 2

vertical shift down two units
horizontal shift right two units
horizontal shift left two units
vertical stretch by factor of 2

Answer 3

I think its A or B

Answer 4

They are asking what is the difference between
y = -3cos(x+pi)
and
y= -2 + -3cos(x+pi)

the first equation will give you some y value, call it y0
the second equation will give you -2 + y0 or y0 - 2
in other words, its y will be two less than y0
is that up or down or sideways?
(remember y measures up/down)

Answer 5

vertical shift down 2 units

Answer 6

yes

Answer 7

awesome one more question then done?

Answer 8

which function has range (-infinity,0) U (2, infinity)? y = csc(x) -1; y = sec(x) + 1 ; y = cot(2x) - 1 ; y = cos(x+ 1)

Answer 9

y = csc(x) - 1?

Answer 10

or y = cot(2x) -1?

Answer 11

the range are the y values you get. That rules out cos() which gives -1 to +1

Answer 12

ok

Answer 13

I'm thinking y = cot(2x) + 1?

Answer 14

y= csc(x) -1 is the same as
y= 1/sin(x) - 1

look at values like -e (a tiny negative #) you get 1/-tiny # = - big #
it goes to -1 - 1 = -2 so (-inf, -2]
there is more, but so far that does not match your question.

Answer 15

sooo it would be csc(x) -1?

Answer 16

or maybe a typing error?

Answer 17

probably... cot() goes -infinity to + infinity

Answer 18

you should check y = sec(x) + 1

y= 1/cos(x) + 1
at x=0 you get 1/1+1 = 1+1 = 2
when you get to x=pi/2, you get 1/0 --> + infinity
so [2, +inf) is part of the range and that matches the question

check the negative #s: when x= pi/2+e you get -infinity
when x= pi you get 0
so (-inf, 0) is the other part of the range

Answer 19

so y = sec (x) + 1?

Answer 20

yes