Question

Which function will have a y-intercept at -1 and an amplitude of 2?

Rx) = -sin(x) - 1
f(x) = -2 sin(x) - 1
f(x) = -cos(x)
f(x) = -2 cos(x) - 1

Answer 1

B

Explanation:

Answer 2

`f(x)=-2sin(x)-1`

Explanation:

For a function to have a y-intercept of -1, means that

when x = 0, f(0) = -1.

we must look for which of the options meets this condition.

I will number the options as follows:

`1. f(x) = -sin(x) - 1\\2.f(x) = -2 sin(x) - 1\\3.f(x) = -cos(x)\\4. f(x) = -2 cos(x) - 1`

• for function 1.

when x = 0:

`f(0)=-sin(0)-1\\`

Note:
`sin(0)=0`, so

`f(0)=0-1\\f(0)=-1`

function 1 meets the condition for the y-intercept.

• for function 2.

when x = 0

`f(0)=-2sin(0)-1\\f(0)=0-1\\f(0)=-1`

function 2 also meets the condition for the y-intercept.

• for function 3.

when x = 0

`f(0)=-cos(0)`

Note:
`cos(0)=1`

`f(0)=-1`

function 3 also meets the condition for the y-intercept.

• for function 4.

when x = 0

`f(0)=-2cos(0)-1\\f(0)=-2(1)-1\\f(0)=-2-1\\f(0)=-3`

function 4 does not meet the condition for the y-intercept, so we discard it.

We are left with the 3 first functions as options. Now we consiser that the amplited must be 2.

The amplitude in an oscillatory function like these is the number that accompanies the sine or the cosine:

f(x) = ±Asin(x) or

f(x) = ±Acos(x)

so out of the option we have to consider, only the second function has a number 2 next to the sine function:

`f(x)=-2sin(x)-1` this function will have a y-intercept of -1 and an amplitude of 2 (because the sine has a number 2 next to it)