Transformation with Function Lesson 1

Problem:   Write the equation for the graph of function g(x), obtained by Shifting

the graph of f(x) = 3x2 three units left, stretching the graph

Vertically by a factor of six, reflecting that result over the x-axis,

and then translating the graph down three units.

Solution     The original function, f(x) is graphed in red.

Step 1:         f(x) with three units to left a vertical stretch

By a factor of 6 is graphed. f(x) with the vertical

Stretch and the translation of 3 units to down

is graphed in green.

Solution     The final transformed function is represented by the equation

Step 2:

Solution     f(x) =-6(x+3)2-3

Step 3:

Solution     A vertical stretch will change the y values. A translation to

Step 4:         the right will affect the x values.

Step 5:

Complete

Try two practice problems:

Solve the following:

 A. Given function f (x)= x2, sketch the graphs of and describe the transformation :f(2x) B. Determine if the functions f(x) and g(x) are odd, even or neither: f(x)= ∣x∣+2 and  g(x) = ∣x+2∣