Question

Please help if you can ASAP! Thanks

Answer 1

Answer:

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

Step-by-step explanation:

Given:

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

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

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

$g(x)=3\sin (\frac{x}{4})+2$

The function 'g' can be rewritten as:

$g(x)=3\sin (\frac{x}{4})+1+1$

So, the 'x' value of 'f' is multiplied by $\frac{1}{4}$ 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 $g(x)$.