functions

Question 1

domain and range of sin

Answer 1

domain = R
Range = [-1,1]

Question 2

domain and range of cos

Answer 2

domain = R
Range = [-1,1]

Question 3

domain and range of tan

Answer 3

domain = R \ {pi/2 +kpi : k E Z }
Range = R

Question 4

domain and range of sec

Answer 4

domain = R \ {pi/2 +kpi : k E Z }
Range = R \ (-1,1)

Question 5

domain and range of csc

Answer 5

domain = R \ {kpi : k E Z }
Range = R \ (-1,1)

Question 6

domain and range of cot

Answer 6

domain = R \ {pi/2 +kpi : k E Z }
Range = R

Question 7

domain and range of cot-1

Answer 7

domain = R
Range = (0, pi)

Question 8

domain and range of sin-1

Answer 8

domain = [-1,1]
range = [-pi/2, pi/2]

Question 9

domain and range of cos-1

Answer 9

domain = [-1,1]
range = [0, pi]

Question 10

domain and range of tan-1

Answer 10

domain = R
range = (-pi/2, pi/2)

Question 11

domain and range of sec-1

Answer 11

domain = R \ (-1,1)
range = [0, pi] \ {pi/2}

Question 12

domain and range of csc-1

Answer 12

domain = R \ (-1,1)
range = [-pi/2, pi/2] \ {0}

Question 13

f(x) + c

Answer 13

upwards shift

Question 14

f(x) - c

Answer 14

downwards shift

Question 15

f(x+c)

Answer 15

left shift

Question 16

f(x-c)

Answer 16

right shift

Question 17

cf(x), if c>1

Answer 17

stretched upwards

Question 18

cf(x), if 0<c<1

Answer 18

compressed downwards

Question 19

cf(x), if c = -1

Answer 19

becomes -f(x), which is a reflection in the x-axis

Question 20

f(cx), if c>1

Answer 20

the graph is compressed inwards

Question 21

f(cx), if 0<c<1

Answer 21

stretched outwards

Question 22

f(cx), if c = -1

Answer 22

it becomes f(-x), which is a reflection in the y axis.

Question 23

is sine an odd or even function?

Answer 23

odd

Question 24

is cos an odd or even function?

Answer 24

even

Question 25

is tan an odd or even function?

Answer 25

odd

Question 26

if f(-x) = -f(x) its an

Answer 26

odd function

Question 27

if f(-x) = f(x) its an

Answer 27

even function

Question 28

if f(-x) doesn't equal f(x) or -f(x) then its a

Answer 28

counter example

Question 29

how do you check if a function is one to one ?

Answer 29

set f(x1) = f(x2), we need to prove that x1 = x2.

Question 30

how do you check if a function is onto?

Answer 30

set the equation equal to y and solve for x. if every y works then it is onto.

Question 31

how to approach odd and eve questions

Answer 31

find f(x) - even find -f(x) - odd find f(-x) match them up