Combine vertical operations with one horizontal translation or stretch.
A vertical operation changes outputs; a horizontal operation changes inputs.
For , move horizontally, multiply each output by , then add .
For , divide each input coordinate by , multiply each output by , then add .
Follow the stated order. A later vertical stretch or reflection also changes an earlier vertical translation.
Example 1
Translate 2 right and 1 up, then stretch vertically by scale factor 2.
1.Translate by .
2.Stretch parallel to the -axis by scale factor .
Example 2
Stretch horizontally by scale factor one half, reflect in the -axis, then translate 3 up.
1.Stretch parallel to the -axis by scale factor .
2.Reflect in the -axis.
3.Translate by .
Remember AA SL includes composite transformations. This card uses either a horizontal translation or a horizontal scale; transformations of the form with both are AA HL content.
Your turn
Question 1
Starting with , apply these transformations in order: Translate by . 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 . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 2
Starting with , apply these transformations in order: Stretch parallel to the -axis by scale factor . Then Reflect in the -axis. Then Translate by . Write the new function and find the image of .
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Reflect in the -axis. .Step 3: Translate by . .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 . 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 . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 4
Starting with , apply these transformations in order: Stretch parallel to the -axis by scale factor . Then Reflect in the -axis. Then Translate by . Write the new function and find the image of .
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Reflect in the -axis. .Step 3: Translate by . .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 . 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 . .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 . Write the new function and find the image of .
Answer
Step 1: Translate by . .Step 2: 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: Stretch parallel to the -axis by scale factor . Then Reflect in the -axis. Then Translate by . Write the new function and find the image of .
Answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Reflect in the -axis. .Step 3: Translate by . .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 . Write the new function and find the image of .
Answer
Step 1: Translate by . .Step 2: 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: Stretch parallel to the -axis by scale factor . Then Reflect in the -axis. Then Translate by . Write the new function and find the image of .
Answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Reflect in the -axis. .Step 3: Translate by . .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 . Write the new function and find the image of .
Answer
Step 1: Translate by . .Step 2: Stretch parallel to the -axis by scale factor . .Image .
Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.