Question

How does changing the function from f(x) = 3 sin 2x to g(x) = 3 sin 2x + 5 affect the range of the function?

Answer 1

these are the answers

The function shifts up 3 units, so the range changes from −1 to 1 in f(x) to 2 to 4 in g(x).

The function shifts up 3 units, so the range changes from −3 to 3 in f(x) to 0 to 6 in g(x).

The function shifts up 5 units, so the range changes from −1 to 1 in f(x) to 4 to 6 in g(x).

The function shifts up 5 units, so the range changes from −3 to 3 in f(x) to 2 to 8 in g(x).

Answer 2

@sidsiddhartha

Answer 3

it shiftss up 5 units but id the rate

Answer 4

range means the max and min values between which the function exists
now tell me what are the max and min values of sinx

Answer 5

how can i do that?

Answer 6

maximum value of sinx is 1 which is sin90
and minimum value of sinx is -1 which is sin270
okay with this

Answer 7

yes

Answer 8

so i can write
\[-1\le sinx \le 1\]
ok?

Answer 9

yes :)

Answer 10

this is also true for sin2x so i can also write
\[-1\le \sin2x \le 1\]

Answer 11

ok

Answer 12

now multiply 3 with each terms then it will be
\[-3\le 3\sin2x \le 3\]
ok??

Answer 13

just multiplying 3 it wont affect all right!!

Answer 14

any problem?

Answer 15

so its The function shifts up 5 units, so the range changes from −3 to 3 in f(x) to 2 to 8 in g(x) bc we multiplied by 3?

Answer 16

yeah
so range of 3sin2x is -3 to 3
\[-3 \le 3\sin2x \le3\]
now for range of 3sin2x+5 we have to add 5 with 3sin2x so we will have then
\[-3+5\le 3\sin2x+5 \le 3+5\]
\[2\le 3\sin2x+5 \le8\]
so last option is correct :)

Answer 17

ok thanks :)