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Transformations of Graphs — Easy Worksheet 2
Grade 12 · Whoobee 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 + 3 outside f moves the graph up 3, so add 3 to y: 1 + 3 = 4. x stays 3. So P moves to (3, 4).
✓ Correct!
Not quite. The answer is
💡 The + 3 outside f moves the graph up 3, so add 3 to y: 1 + 3 = 4. x stays 3. So P moves to (3, 4).
💡 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, -4) 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 − 5 moves the graph right 5 (the opposite of the sign you see), so add 5 to x: -4 + 5 = 1. y stays 0. So P moves to (1, 0).
✓ 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: -4 + 5 = 1. y stays 0. So P moves to (1, 0).
💡 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, 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 left 4 (the opposite of the sign you see), so subtract 4 from x: 3 − 4 = -1. y stays 2. So P moves to (-1, 2).
✓ Correct!
Not quite. The answer is
💡 Inside f, x + 4 moves the graph left 4 (the opposite of the sign you see), so subtract 4 from x: 3 − 4 = -1. y stays 2. So P moves to (-1, 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, 1) 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
💡 Inside f, x − 4 moves the graph right 4 (the opposite of the sign you see), so add 4 to x: -3 + 4 = 1. y stays 1. So P moves to (1, 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: -3 + 4 = 1. y stays 1. So P moves to (1, 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(-5, -2) 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 + 2 moves the graph left 2 (the opposite of the sign you see), so subtract 2 from x: 5 − 2 = 3. y stays -4. So P moves to (3, -4).
✓ Correct!
Not quite. The answer is
💡 Inside f, x + 2 moves the graph left 2 (the opposite of the sign you see), so subtract 2 from x: 5 − 2 = 3. y stays -4. So P moves to (3, -4).
💡 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, 4) 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: 2 + 5 = 7. x stays -3. So P moves to (-3, 7).
✓ Correct!
Not quite. The answer is
💡 The + 5 outside f moves the graph up 5, so add 5 to y: 2 + 5 = 7. x stays -3. So P moves to (-3, 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, -2) 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
💡 The + 1 outside f moves the graph up 1, so add 1 to y: -3 + 1 = -2. x stays 3. So P moves to (3, -2).
✓ Correct!
Not quite. The answer is
💡 The + 1 outside f moves the graph up 1, so add 1 to y: -3 + 1 = -2. x stays 3. So P moves to (3, -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(4, -2) 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 = 3. y stays 0. So P moves to (3, 0).
✓ 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 = 3. y stays 0. So P moves to (3, 0).
💡 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(0, 1) 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.
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Transformations of Graphs — Easy Worksheet 2
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).