The graph of f(x)=sin(x) is transformed into a new function, g(x), by stretching it vertically by a factor of 4 and shifting it 3 units to the right.
What is the equation of the new function g(x)?
if you stretch it out by a factor of 4, it means that the x values change only 1/4 as fast.
sin(1/4 x) means you now have to have 4 times the value of x to get to the same place.
Similarly, you have to subtract 3 from the new x to get the original y.
So,
g(x) = sin(1/4 (x-3))
you can see the results here:
https://www.wolframalpha.com/input/?i=plot+y%3Dsinx,+y%3Dsin(1%2F4+(x-3))
But y = sinx stretched vertically by a factor of 4 and shifted 3 units to the right would be
y = 4sin(x-3)
see:
see:
https://www.wolframalpha.com/input/?i=plot+y%3Dsinx,+y%3D+4sin(x-3)
To find the equation of the new function g(x) that is a transformation of f(x)=sin(x), we need to apply the given transformations.
The given transformations are:
1. Vertical stretching by a factor of 4.
2. Horizontal shift 3 units to the right.
Let's examine each transformation step by step:
1. Vertical Stretching by a factor of 4:
When we vertically stretch a graph, we multiply the y-values (output values) by the stretching factor. In this case, since the stretching factor is 4, we multiply the f(x) by 4.
Therefore, the new equation after vertical stretching becomes f(x) = 4 * sin(x).
2. Horizontal Shift 3 units to the right:
When we horizontally shift a graph, we change the x-values (input values). In this case, since the shift is 3 units to the right, we subtract 3 from x.
Therefore, the final equation after the horizontal shift becomes:
g(x) = 4 * sin(x - 3).
Hence, the equation of the new function g(x) is g(x) = 4 * sin(x - 3).