- Compare horizontal distances between corresponding points to find the horizontal scale factor. Then find the horizontal translation.
- Use vertical distances and vertical positions in the same way. Check every labelled point against the final function.
The intercepts A(−4, 0), B(0, 0) and C(6, 0) become A(−10, 0), B(−2, 0) and C(10, 0). Write the new function, then play to check.
1.Stretch parallel to the -axis by scale factor .
AB doubles from 4 to 8 and BC doubles from 6 to 12. Use a horizontal stretch of 2, then shift 2 left: .
The points A(−2, 0), B(0, −4) and C(2, 0) become A(−2, 3), B(0, −5) and C(2, 3). Write the new function, then play to check.
1.Stretch parallel to the -axis by scale factor .
The vertical gap from B to A doubles from 4 to 8. Original zero outputs finish at 3, so .
Remember
Use distances to identify the stretch, then a point to identify the translation. Checking several points helps rule out a mistaken order.
Your turn
5 practice questions 0 of 5 answers checked
Question 1The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 2The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 3The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 4The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
Question 5The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
Check answer
Step 1: Stretch parallel to the -axis by scale factor . .Step 2: Reflect in the -axis. .Step 3: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
AnswerStep 1: Stretch parallel to the -axis by scale factor . .Step 2: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
AnswerStep 1: Stretch parallel to the -axis by scale factor . .Step 2: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
AnswerStep 1: Stretch parallel to the -axis by scale factor . .Step 2: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
AnswerStep 1: Stretch parallel to the -axis by scale factor . .Step 2: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.
The black graph is . The blue graph is its image. Use the corresponding points to describe the transformations and write the new function.
AnswerStep 1: Stretch parallel to the -axis by scale factor . .Step 2: Reflect in the -axis. .Step 3: Translate by . . Horizontal operations act on the current -coordinates; vertical operations act on the current -coordinates.