Question

The graph of f(x)=sin(x) is transformed to a new function, g(x) , by stretching it vertically by a factor of 2 and shifting it 3 units up. What is the equation of the new function g(x) ? Enter your answer in the box.

Answer 1

Answer:

$g(x)=2sinx+3$

Step-by-step explanation:

The sine function has the general equation

$y=A *sin(kx+b)+h$ where

• A is the amplitude or vertical stretch
• k is the period factor
• b is the horizontal shift
• h is the vertical stretch

We start with $f(x)=sinx$ were A=1 and h=0. We transform the function by multiplying A by 2 for a vertical stretch. A=1(2)=2. A is now 2.

We finish transforming the function by shifting it up 3 units. This means h=0 becomes 0+3=3. H is now 3.

Our new function is $g(x)=2sinx+3$.