# FNGR 2 | Lesson 4 | Making Connections

You have experienced transformations with both exponential functions and with quadratic functions. Does this apply to any function? Go to Desmos and try the following functions:

1. $$f(x) = x^3$$
2. $$f(x) = x^3 + 2$$. Compare this to #1, how is it different?
3. $$f(x) = (x-1)^3$$. Compare this to #1, how is it different?
4. $$f(x) = (x + 1)^3 -2$$. Compare this again to #1, how is it different?
5. $$f(x) = 2x^3$$. Again compare this to #1 and describe the difference.
6. Given the function $$f(x)$$, Describe what happens in the graph of $$f(x) = 2 (x-1)^2 -3$$.

Did you see that #2 is a vertical translation, #3 is a horizontal translation, #4 has both a vertical and a horizontal translation, #5 is a dialation (each point in the original is multiplied by 2 and #6 has a vertical translation down 3, horizontal translation right 1 and a dialation.

For additional information and check, go to Khan Academy video: Identifying Transformations. You may also want to check out the Practice .

Can you generalize this to any function? You could go to Desmos again and try it with a quartic, a trigonometric function. What do you see?

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