- Write the function in the form , with and .
- The horizontal scale factor is . If , also reflect in the -axis. The translation in the factorised input is .
- The vertical scale factor is . If , also reflect in the -axis. One reliable choice is stretches and reflections first, then translate by .
Example 1
Describe transformations taking to .
1. Stretch parallel to the -axis by scale factor .2. Stretch parallel to the -axis by scale factor .3. Translate by . Here . The horizontal translation is 2 right, not 4 right. A scale factor of halves every horizontal distance.
Example 2
Describe transformations taking to .
1. Stretch parallel to the -axis by scale factor .2. Reflect in the -axis.3. Reflect in the -axis.4. Translate by . Factorise . The minus inside gives a reflection in the -axis; the minus outside gives a reflection in the -axis.
Remember
A function gives a target graph. You may choose a valid order. A worded instruction that says “then” fixes the order you must follow.
Your turn
5 practice questions 0 of 5 answers checked
Question 1Fully 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 2Fully 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 3Fully 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 4Fully 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 5Fully 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 .
AnswerStep 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 .
AnswerStep 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 .
AnswerStep 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 .
AnswerStep 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 .
AnswerStep 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.