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Transformations of Functions — Easy Worksheet 1
Grade 11 · Whoobee Name: ____________________ Date: __________
Use the rules for shifts, stretches and reflections.
How to solve
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Example
The graph of y = |x| is shifted 2 units right. Write the equation of the new graph.
Answer: y = |x - 2|
Not quite. The answer is
💡 Use y = a·f(x − h) + k with f(x) = x². Shifting 2 left makes h = −2, so x is replaced by x + 2. Shifting 2 up makes k = 2, so add 2 at the end. So y = (x + 2)² + 2.
✓ Correct!
Not quite. The answer is
💡 Use y = a·f(x − h) + k with f(x) = x². Shifting 2 left makes h = −2, so x is replaced by x + 2. Shifting 2 up makes k = 2, so add 2 at the end. So y = (x + 2)² + 2.
💡 How to solve: Transformations of Functions
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Try a similar one
The graph of y = x³ is shifted 4 units left, then shifted 3 units down. Write the equation of the new graph.
✓ 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 vertex of the V (its lowest point) is at (−2, −2), so h = −2 and k = −2. It opens upward like y = |x|, so a = 1. Use y = a·f(x − h) + k: y = |x + 2| − 2. Check: one unit right of the vertex, at x = −1, the graph is at y = −1.
✓ Correct!
Not quite. The answer is
💡 The vertex of the V (its lowest point) is at (−2, −2), so h = −2 and k = −2. It opens upward like y = |x|, so a = 1. Use y = a·f(x − h) + k: y = |x + 2| − 2. Check: one unit right of the vertex, at x = −1, the graph is at y = −1.
💡 How to solve: Transformations of Functions
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Try a similar one
The graph of y = x³ is shifted 6 units right, then shifted 5 units down. Write the equation of the new graph.
✓ 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
💡 Use y = a·f(x − h) + k with f(x) = x³. Shifting 4 right makes h = 4, so x is replaced by x − 4. Shifting 6 down makes k = −6, so subtract 6 at the end. So y = (x − 4)³ − 6.
✓ Correct!
Not quite. The answer is
💡 Use y = a·f(x − h) + k with f(x) = x³. Shifting 4 right makes h = 4, so x is replaced by x − 4. Shifting 6 down makes k = −6, so subtract 6 at the end. So y = (x − 4)³ − 6.
💡 How to solve: Transformations of Functions
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Try a similar one
The graph of y = x² is shifted 1 unit left, then shifted 5 units down. Write the equation of the new graph.
✓ 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 inside f(x − 5) shifts the graph 5 right, so add 5 to x: −5 + 5 = 0. The outside adds −3 to y: 0 + (−3) = −3. The new point is (0, −3).
✓ Correct!
Not quite. The answer is
💡 The inside f(x − 5) shifts the graph 5 right, so add 5 to x: −5 + 5 = 0. The outside adds −3 to y: 0 + (−3) = −3. The new point is (0, −3).
💡 How to solve: Transformations of Functions
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Try a similar one
The graph of y = |x| is shifted 4 units left, then shifted 2 units down. Write the equation of the new graph.
✓ 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
💡 Use y = a·f(x − h) + k with f(x) = x³. Shifting 2 right makes h = 2, so x is replaced by x − 2. Shifting 1 down makes k = −1, so subtract 1 at the end. So y = (x − 2)³ − 1.
✓ Correct!
Not quite. The answer is
💡 Use y = a·f(x − h) + k with f(x) = x³. Shifting 2 right makes h = 2, so x is replaced by x − 2. Shifting 1 down makes k = −1, so subtract 1 at the end. So y = (x − 2)³ − 1.
💡 How to solve: Transformations of Functions
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Try a similar one
The graph of y = x³ is shifted 4 units right, then shifted 5 units down. Write the equation of the new graph.
✓ 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 vertex of the V (its lowest point) is at (2, 2), so h = 2 and k = 2. It opens upward like y = |x|, so a = 1. Use y = a·f(x − h) + k: y = |x − 2| + 2. Check: one unit right of the vertex, at x = 3, the graph is at y = 3.
✓ Correct!
Not quite. The answer is
💡 The vertex of the V (its lowest point) is at (2, 2), so h = 2 and k = 2. It opens upward like y = |x|, so a = 1. Use y = a·f(x − h) + k: y = |x − 2| + 2. Check: one unit right of the vertex, at x = 3, the graph is at y = 3.
💡 How to solve: Transformations of Functions
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Try a similar one
The graph of y = |x| is shifted 1 unit left, then shifted 6 units up. Write the equation of the new graph.
✓ 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
💡 Use y = a·f(x − h) + k with f(x) = x³. Shifting 5 right makes h = 5, so x is replaced by x − 5. Shifting 1 down makes k = −1, so subtract 1 at the end. So y = (x − 5)³ − 1.
✓ Correct!
Not quite. The answer is
💡 Use y = a·f(x − h) + k with f(x) = x³. Shifting 5 right makes h = 5, so x is replaced by x − 5. Shifting 1 down makes k = −1, so subtract 1 at the end. So y = (x − 5)³ − 1.
💡 How to solve: Transformations of Functions
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Try a similar one
The graph of y = |x| is shifted 1 unit right, then shifted 5 units down. Write the equation of the new graph.
✓ 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 inside f(x + 5) shifts the graph 5 left, so add −5 to x: −4 + (−5) = −9. The outside adds 2 to y: −3 + 2 = −1. The new point is (−9, −1).
✓ Correct!
Not quite. The answer is
💡 The inside f(x + 5) shifts the graph 5 left, so add −5 to x: −4 + (−5) = −9. The outside adds 2 to y: −3 + 2 = −1. The new point is (−9, −1).
💡 How to solve: Transformations of Functions
For g(x) = a·f(x - h) + k: h moves the graph right (h > 0) or left, k moves it up or down, |a| > 1 stretches it vertically, and a negative a reflects it across the x-axis. A point (x, y) on f moves to (x + h, a·y + k) on g.
Try a similar one
The graph of y = x³ is shifted 3 units left, then shifted 3 units up. Write the equation of the new graph.
✓ 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 Functions — Easy Worksheet 1
Use the rules for shifts, stretches and reflections.