02Btransformcubic

toc = Transformations and the Cubic =

We can apply the standard transformations such as dilations, translations and reflections when sketching a cubic graph from a cubic equation in standard form.

** Example **
State the changes necessary to transform the graph of y = x 3 into the graph of the following.


 * a) ** y = 4 – 2x 3.


 * Reflection across the x-axis (in the y-direction)
 * Dilation in the y direction by a factor of 2
 * Translation up by 4 units


 * b) ** y = (2 – 3x) 3.

This can be written as: math y = \Big( -3 \left( x - \frac{2}{3} \right) \Big)^3 math


 * Reflection across the y-axis (in the x-direction)
 * Dilation in the x direction by a factor of 1/3
 * Translation by 2/3 units to the right

but it is standard to state the reflection or dilation first and then the translation. Go to top of page flat .
 * Note: ** The transformations described in (b) are equivalent to (starting with the standard cubic):
 * x-values subtract 2, then divide by –3
 * y-values unchanged