1. Transformation of Graphs
Literacy
Research
Memory
Define each transformation.
𝑓 𝑥 →
𝑓 𝑎𝑥 , 𝑓 𝑥+𝑎 , 𝑎𝑓 𝑥 ,
−𝑓 𝑥 , 𝑓 −𝑥 , 𝑓 𝑥 +𝑎
Sound waves are similar to sine and cosine graphs. If a sound created the function 𝑓(𝑥), find out what effect on the sound 𝑎𝑓(𝑥) & 𝑓 𝑎𝑥 has.
Find out how noise cancellation works in terms of transformations.
Sketch the graphs of:
𝑓 𝑥 = 1 𝑥 2
𝑓 𝑥 = 1 𝑥
𝑓 𝑥 = 𝑥 2
𝑓 𝑥 = 𝑥 3
𝑓 𝑥 = 𝑥
Key words: stretch, vector, scale factor, reflection, translation, parallel, axis
You will need to know the shapes and any asymptotes of these graphs in order to transform them!
Skills Practice
Stretch
Let 𝑓 𝑥 = 1 𝑥 , sketch the graphs of: (i) 𝑓 −𝑥 (ii)𝑓 𝑥 −3
The graph 𝑓 𝑥 = 1 𝑥 2 has been translated by two places in the negative x direction. What is the new function?
Give one example of a transformation that maps 𝑓 𝑥 =𝑠𝑖𝑛𝑥 to 𝑔 𝑥 =𝑐𝑜𝑠𝑥.
ℎ 𝑥 = 𝑥 2 . 𝑗 𝑥 = 𝑥 2 +5𝑥−3. Describe the transformation that maps ℎ 𝑥 to 𝑗 𝑥
1. Describe how to sketch the graph of 𝑦=−2𝑓 2𝑥 +4.
2. Starting with a graph 𝑦=𝑓(𝑥), if we shift it to the left by 3 and then stretch it horizontally by 2, what graph do we end up with?
3. With the same graph, what do we end up with if stretch horizontally by 2 first, then shift to the left by 3?
4. If 𝑓 𝑥 = 1 𝑥 . What other transformation transforms 𝑓(𝑥) in the same way that −𝑓(𝑥) does? 5.
Let f(x) be shown in figure 3. Sketch the graphs and label the transformations of the coordinates from figure 3:
0.5𝑓(𝑥) 𝑓( 𝑥 3 ) 𝑓(2𝑥+1)