Build the new function one instruction at a time, then track its key points.
To translate right, replace every in the current expression with . To stretch horizontally by , replace every with .
For a vertical stretch, multiply the whole current output. For a vertical translation, add to that output.
Example 1
Translate 2 left and 1 up, then stretch horizontally by scale factor 2, then stretch vertically by scale factor 3.
1.Translate by .
2.Stretch parallel to the -axis by scale factor .
3.Stretch parallel to the -axis by scale factor .
The functions are , then , then . Both parts of the original translation are affected.
Example 2
Reflect in the -axis, translate 2 right and 3 down, then stretch vertically by scale factor 3.
1.Reflect in the -axis.
2.Translate by .
3.Stretch parallel to the -axis by scale factor .
The last operation gives . The downward translation is stretched too.
Remember When the question gives an order, write the intermediate function after every instruction.
Your turn
5 practice questions
0 of 5 answers checked
Question 1
Starting with , apply these transformations in order: Translate by . Then Stretch parallel to the -axis by scale factor . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Check answer
Step 1: Translate by . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 2
Starting with , apply these transformations in order: Reflect in the -axis. Then Translate by . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Check answer
Step 1: Reflect in the -axis. .Step 2: Translate by . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 3
Starting with , apply these transformations in order: Translate by . Then Stretch parallel to the -axis by scale factor . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Check answer
Step 1: Translate by . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 4
Starting with , apply these transformations in order: Reflect in the -axis. Then Translate by . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Check answer
Step 1: Reflect in the -axis. .Step 2: Translate by . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 5
Starting with , apply these transformations in order: Translate by . Then Stretch parallel to the -axis by scale factor . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Check answer
Step 1: Translate by . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Starting with , apply these transformations in order: Translate by . Then Stretch parallel to the -axis by scale factor . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Answer
Step 1: Translate by . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Starting with , apply these transformations in order: Reflect in the -axis. Then Translate by . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Answer
Step 1: Reflect in the -axis. .Step 2: Translate by . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Starting with , apply these transformations in order: Translate by . Then Stretch parallel to the -axis by scale factor . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Answer
Step 1: Translate by . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Starting with , apply these transformations in order: Reflect in the -axis. Then Translate by . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Answer
Step 1: Reflect in the -axis. .Step 2: Translate by . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Starting with , apply these transformations in order: Translate by . Then Stretch parallel to the -axis by scale factor . Then Stretch parallel to the -axis by scale factor . Write the new function and find the image of .
Answer
Step 1: Translate by . .Step 2: Stretch parallel to the -axis by scale factor . .Step 3: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.