Use a clear sequence to sketch a function transformed in both directions.
Factorise the input. Choose stretches and reflections first, then the translation.
A horizontal operation and a vertical operation can swap order because they change different coordinates. Keep track of translations in the same direction.
Example 1
Sketch .
1.Stretch parallel to the -axis by scale factor .
2.Stretch parallel to the -axis by scale factor .
3.Translate by .
The point B(0, −4) moves to B(0, −4), then B(0, −12), then B(2, −5). The whole graph follows the same operations.
Example 2
Sketch . Factor the input as .
1.Stretch parallel to the -axis by scale factor .
2.Reflect in the -axis.
3.Stretch parallel to the -axis by scale factor .
4.Translate by .
Use horizontal scale factor 2, reflect in the -axis, use vertical scale factor 2, then move 1 left and 3 down.
Remember The final translation is read from the factorised input and the term added outside the function.
Your turn
5 practice questions
0 of 5 answers checked
Question 1
Fully describe one sequence mapping to . Then find the image of .
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 2
Fully describe one sequence mapping to . Then find the image of .
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 3
Fully describe one sequence mapping to . Then find the image of .
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 4
Fully describe one sequence mapping to . Then find the image of .
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 5
Fully describe one sequence mapping to . Then find the image of .
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Fully describe one sequence mapping to . Then find the image of .
Answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Fully describe one sequence mapping to . Then find the image of .
Answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Fully describe one sequence mapping to . Then find the image of .
Answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Fully describe one sequence mapping to . Then find the image of .
Answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Fully describe one sequence mapping to . Then find the image of .
Answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Translate by . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.