The same function using different transformation orders
Choose different valid orders by adjusting the translation.
Different orders can produce the same graph, but the translation usually needs to change.
Check the intermediate functions and the final positions of corresponding points.
Example 1
Stretch first
Produce by stretching first.
1.Stretch parallel to the -axis by scale factor .
2.Translate by .
Halve the -coordinates, then add 3. The result is .
Example 2
Translate first
Produce the same function , but translate first.
1.Translate by .
2.Stretch parallel to the -axis by scale factor .
Move 6 right, then halve the -coordinates. The result is again . A 3-right move before the stretch would give .
Remember If you move the translation earlier, account for how the later stretch or reflection will change it.
Your turn
5 practice questions
0 of 5 answers checked
Question 1
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Check answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 2
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Check answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 3
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Check answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 4
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Check answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 5
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Check answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
For , describe one sequence with the horizontal stretch first and another with the translation first. Check the image of .
Answer
Stretch first: Stretch parallel to the -axis by scale factor . Then Translate by .Translate first: Translate by . Then Stretch parallel to the -axis by scale factor .Both give , with .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.