Expert: Sherry Wallin - 11/5/2009

Question
how to list the transformations applied to parent function f(x)=x^4 to obtain g(x)=-2(x-3)^4+5

Answer
Hi Chanae~
    Beginning with the function f(x) = x^4 your g(x) is obtained by realizing that the leading coefficient -2 flips it from facing up to facing down and increases the x values by a factor of |-2| = 2 which essentially 'widens' the graph (grows faster in the x direction) and the x-3 shifts x to the right 3 units, and the +5 moves the whole function up 5 units. If you are looking for what order to go from f(x) to g(x) then you want to first work inside the parentheses and so you would first subtract 3 from the x, then raise the (x-3) to the fourth power and then add 5 to the result.

    I hope this is what you meant by listing the transformations. Otherwise please ask me again and tell me more specifically what you want.

Math Prof