Precalc
HW
Transformations and Function Notation
For each section of problems 1 and 2 draw a graph first (on graph paper without the aid of a
graphing calculator) and then write the equation which represents the new function. After you
have graphed by hand then check your graphs with your graphing calculator. Remember you can
use the VARS menu to use Y1, Y2 etc. and function notation in the equation editor of your
calculator.
1. Start with f (x) = x 2
a) Graph g(x) = - f (x)+ 3
Equation: ___________________
b) Graph h(x) = -g(x - 2)
Equation: ___________________
(make sure you are using the g function from part a) and not the f function again!)
c) Graph i(x) = h(-x) - 2
Equation: ___________________
d) Graph j(x) = i(2 - x)
Equation: ___________________
2. Start with f (x) = x
a) Graph g(x) = f (-x) - 2
Equation: ___________________
b) Graph h(x) = -g(x - 3)
Equation: ___________________
c) Graph i(x) = -h(x)+ 4
Equation: ___________________
d) Graph j(x) = 2i(x -1)
Equation: ___________________
3. Start with f(x) graphed on the right:
a) Graph g(x) = - f (-x)
b) Graph h(x) = g(x + 3)+1
c) Graph i(x) = h(2 - x)
d) Graph j(x) = i(2x)
4. Start with f (x) = x . Create four instructions using function notation similar to the problems
above in which each instruction contains at least 2 transformations so that the last graph ends up
as j(x) = - 2 - x + 3
g(x) = _________________________
h(x) = _________________________
i(x) = __________________________
j(x) = __________________________