Question

Please help if you can ASAP! Thanks

Answer 1

The graph stretches horizontally by a factor of 4 and shifted up by 1 unit.

Explanation:

Given:

The function
`f(x)` is given as:

`f(x)=3\sin (x)+1`

The function
`g(x)` is given as:

`g(x)=3\sin ((x)/(4))+2`

The function 'g' can be rewritten as:

`g(x)=3\sin ((x)/(4))+1+1`

So, the 'x' value of 'f' is multiplied by
`(1)/(4)` and 1 unit is added to the function to get the function 'g'.

Therefore, as per transformation rules:

1.
`f(x)\to f(Cx)`

• If C > 1 ⇒ The graph compresses in the x direction.
• If 0 < C < 1 ⇒ The graph stretches in the x direction by factor of 1/C.

2.
`f(x)\to f(x)+C`

• If C > 0 ⇒ The graph shifts up by 'C' units.
• If C < 0 ⇒ The graph shifts down by 'C' units.

Therefore, the graph of
`f(x)` stretches in the x direction(horizontally) by a factor of 4 and shifts up by 1 unit to get
`g(x)`.