Or press and hold the picture and choose “Save image”.
for Whoobee's shop
Transformations of Graphs — Easy Worksheet 1
Grade 12 · MathSheets Name: ____________________ Date: __________
The point P is on the graph of y = f(x). Find the point it moves to on the new graph. Write the answer as (x, y).
How to solve
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Example
P(-1, -5) is on the graph of y = f(x). Which point must be on the graph of y = f(x) + 4?
Answer: (-1, -1)
Not quite. The answer is
💡 The + 1 outside f moves the graph up 1, so add 1 to y: 2 + 1 = 3. x stays 0. So P moves to (0, 3).
✓ Correct!
Not quite. The answer is
💡 The + 1 outside f moves the graph up 1, so add 1 to y: 2 + 1 = 3. x stays 0. So P moves to (0, 3).
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(-2, 5) is on the graph of y = f(x). Which point must be on the graph of y = f(x) + 3?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The + 5 outside f moves the graph up 5, so add 5 to y: -4 + 5 = 1. x stays 0. So P moves to (0, 1).
✓ Correct!
Not quite. The answer is
💡 The + 5 outside f moves the graph up 5, so add 5 to y: -4 + 5 = 1. x stays 0. So P moves to (0, 1).
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(-3, 3) is on the graph of y = f(x). Which point must be on the graph of y = f(x + 1)?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Inside f, x − 4 moves the graph right 4 (the opposite of the sign you see), so add 4 to x: 1 + 4 = 5. y stays -1. So P moves to (5, -1).
✓ Correct!
Not quite. The answer is
💡 Inside f, x − 4 moves the graph right 4 (the opposite of the sign you see), so add 4 to x: 1 + 4 = 5. y stays -1. So P moves to (5, -1).
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(3, 1) is on the graph of y = f(x). Which point must be on the graph of y = f(x) - 4?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Inside f, x − 5 moves the graph right 5 (the opposite of the sign you see), so add 5 to x: -2 + 5 = 3. y stays -3. So P moves to (3, -3).
✓ Correct!
Not quite. The answer is
💡 Inside f, x − 5 moves the graph right 5 (the opposite of the sign you see), so add 5 to x: -2 + 5 = 3. y stays -3. So P moves to (3, -3).
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(-2, 5) is on the graph of y = f(x). Which point must be on the graph of y = f(x) - 2?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The − 4 outside f moves the graph down 4, so subtract 4 from y: 3 − 4 = -1. x stays -3. So P moves to (-3, -1).
✓ Correct!
Not quite. The answer is
💡 The − 4 outside f moves the graph down 4, so subtract 4 from y: 3 − 4 = -1. x stays -3. So P moves to (-3, -1).
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(2, 3) is on the graph of y = f(x). Which point must be on the graph of y = f(x - 5)?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Inside f, x + 3 moves the graph left 3 (the opposite of the sign you see), so subtract 3 from x: -5 − 3 = -8. y stays -2. So P moves to (-8, -2).
✓ Correct!
Not quite. The answer is
💡 Inside f, x + 3 moves the graph left 3 (the opposite of the sign you see), so subtract 3 from x: -5 − 3 = -8. y stays -2. So P moves to (-8, -2).
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(-5, 0) is on the graph of y = f(x). Which point must be on the graph of y = f(x - 4)?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The + 4 outside f moves the graph up 4, so add 4 to y: -3 + 4 = 1. x stays -3. So P moves to (-3, 1).
✓ Correct!
Not quite. The answer is
💡 The + 4 outside f moves the graph up 4, so add 4 to y: -3 + 4 = 1. x stays -3. So P moves to (-3, 1).
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(2, -3) is on the graph of y = f(x). Which point must be on the graph of y = f(x - 2)?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The − 2 outside f moves the graph down 2, so subtract 2 from y: -5 − 2 = -7. x stays -5. So P moves to (-5, -7).
✓ Correct!
Not quite. The answer is
💡 The − 2 outside f moves the graph down 2, so subtract 2 from y: -5 − 2 = -7. x stays -5. So P moves to (-5, -7).
💡 How to solve: Transformations of Graphs
Changes outside f act on y: +k moves up, -f flips over the x-axis, a·f stretches y by a. Changes inside act on x the opposite way: f(x - h) moves right h, f(-x) flips over the y-axis, f(bx) divides x by b.
Try a similar one
P(1, -5) is on the graph of y = f(x). Which point must be on the graph of y = f(x) - 5?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Log in to save your progress.
Transformations of Graphs — Easy Worksheet 1
The point P is on the graph of y = f(x). Find the point it moves to on the new graph. Write the answer as (x, y).