Transform sine vertically, stretch and translate together
- Lee W Fisher
Graph 1: Vertical Stretch, Vertical Translation
1. Order of operations
Suppose you wish to transform to . Does it make mathematical sense to 1. stretch (multiply y values by 3) then to translate (add 5 to all new y values)? or to 2. translate (add 5 to all y values) then to stretch (multiply new y values by 3)? (Hint - take the point as an example - does the y value become or ?)
Graph 2 has equation where . Which one of the following is a correct equation for this function?
What is the range of the function , shown in graph 2?
The graph of the function where is shown in graph 3. What is the equation of the function ?
What is the range of the function ?
The function is defined . What is the range of ?