Transformation with Function
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
Solution f(x) =-6(x+3)2-3
Solution A vertical stretch will change the y values. A translation to
Step 4: the right will affect the x values.
Solution Answer is: -6(x+3)2-3
Try two practice problems:
Solve the following: