Question

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) ? Enter your answer in the box.

Answer 1

If we compress the graph of $y = sin x$ vertically by 1/2, this gives us the equation $y = \frac{1}{2} sin x$. Shifting this downward (vertically) by 3 units will mean that the expression must have 3 subtracted from it, leaving the final equation of g(x) to be:
$g(x) = \frac{1}{2} sin x - 3$