What sine function represents an amplitude of 1, a period of 2π, a horizontal shift of π, and a vertical shift of −4?
Select one:
a. f(x) = sin (x − π) − 4
b. f(x) = sin (πx) + 4
c. f(x) = sin (x + pi over 2 ) + 4
d. f(x) = sin ( pi over 2 x) − 4

Option a. f(x) = sin (x - ) - 4 is the required sine function

Step-by-step explanation:

Step 1 :

Given,

Amplitude = 1

period = 2

horizontal shift =

Vertical shift = -4

Step 2 :

The sine function's equation is as follows :

f(x) = a sin(bx + c) + d

where

a represents the amplitude

b represents the period, obtained by dividing the given period by 2

c represents the horizontal shift

d represents the vertical shift

Step 3:

So here we have,

a = 1

b = 2 / 2 = 1

c = - (assuming the wave is shifted to the right)

d= -4

Substituting the values in the sine function we get

f(x) = sin (x - ) - 4

Step 4:

Answer

option a. f(x) = sin (x - ) - 4 is the required sine function

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

true

step-by-step explanation: