The graph of f(x)=sin(x) is transformed into a new function, g(x) , by compressing it vertically by a factor of 1/2 and shifting it 3 units down.
What is the equation of the new function g(x) ?
compress by 1/2: g = 1/2 sin(x)
shift down 3: g = 1/2 sin(x)-3
g(x) = 1/2 f(x) - 3
To find the equation of the new function g(x), which is created by compressing the graph of f(x)=sin(x) vertically by a factor of 1/2 and shifting it 3 units down, we need to apply the transformations to the original equation.
First, we will focus on the vertical compression. The general form of a vertical compression is given by multiplying the function by a constant. In this case, since we want to compress the graph by a factor of 1/2, we will multiply the original function f(x)=sin(x) by 1/2.
So far, the equation of the transformed function is g(x) = (1/2)*sin(x).
Next, we will consider the vertical shift. The general form of a vertical shift is given by adding or subtracting a constant from the function. In this case, we want to shift the graph 3 units down, so we will subtract 3 from the transformed function.
The final equation of the new function g(x) is:
g(x) = (1/2)*sin(x) - 3
Therefore, the equation of the new function g(x) is g(x) = (1/2)*sin(x) - 3.