Question 1 Easy
How many units up does y=f(x)+4 move each point?
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Answer: 4
- The +4 is outside.
- Every y-coordinate increases by 4.
- Method (1): The +4 is outside.
- Accuracy (1): Answer 4
Transforming graphs y = f(x) practice questions with answers
A second set of transforming graphs y = f(x) questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
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Question 2 Easy
A curve passes through (2, 5). Give the image of that point on y=f(x+2).
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Answer: (0, 5)
- The graph moves left.
- Subtract 2 from the x-coordinate.
- Method (1): The graph moves left.
- Accuracy (1): Answer (0, 5)
Question 3 Medium
(4, -1) lies on y=f(x). Write its image on y=f(x-1).
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Answer: (5, -1)
- f(x-1) moves the graph right by 1.
- Add 1 to x and keep y.
- Method (1): f(x-1) moves the graph right by 1.
- Accuracy (1): Answer (5, -1)
Question 4 Medium
(1, 3) lies on y=f(x). Write its image on y=f(x)+2.
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Answer: (1, 5)
- Add 2 to the y-coordinate.
- x stays 1.
- Method (1): Add 2 to the y-coordinate.
- Accuracy (1): Answer (1, 5)
Question 5 Hard
Which equation moves a graph left: f(x+2), f(x-2), or f(x)+2?
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Answer: f(x+2)
- Left comes from a plus inside.
- A plus outside is vertical.
- Method (1): Left comes from a plus inside.
- Accuracy (1): Answer f(x+2)
Question 6 Hard
Which equation reflects y=f(x) in the y-axis?
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Answer: f(-x)
- Swap the sign of the input.
- The output sign is a different mirror.
- Method (1): Swap the sign of the input.
- Accuracy (1): Answer f(-x)
Exam-style question
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
Exam-style question 12 marks
The point (5, -2) lies on y=f(x). Find its image on y=f(x-2)+3.
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Answer: (7, 1)
- f(x-2) moves the point right by 2.
- Then +3 raises it.
- Image (7, 1).
- Mark (1): x-coordinate 7
- Mark (1): y-coordinate 1
Quick checks
Short one-step questions. Pick an option before you open the answer.
Check 1
f(x+2) moves a graph which way?
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Left. The plus sign is inside the bracket. Left. The plus sign is inside the bracket.
Check 2
f(x-2) moves a graph which way?
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Right. Subtracting inside shifts the picture right. Right. Subtracting inside shifts the picture right.
Check 3
What changes when you replace f(x) with f(x)+3?
- f(x)+2. The change is outside the bracket.
- (0, 1). The graph has moved left by 5.
- Every point moves up by 3. The shape is the same.
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Every point moves up by 3. The shape is the same. Every point moves up by 3. The shape is the same.
Check 4
The point (2, 7) is on y=f(x). Where is it on y=-f(x)?
- f(x)+2. The change is outside the bracket.
- Every point moves up by 3. The shape is the same.
- (2, -7). Only the height changes sign.
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(2, -7). Only the height changes sign. (2, -7). Only the height changes sign.
Check 5
-f(x) is a reflection in which axis?
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The x-axis. Heights change sign. The x-axis. Heights change sign.
Check 6
f(-x) is a reflection in which axis?
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The y-axis. Left and right swap. The y-axis. Left and right swap.
Check 7
A point (5, 1) is on y=f(x). Where is it on y=f(x+5)?
- f(x)+2. The change is outside the bracket.
- (2, -7). Only the height changes sign.
- (0, 1). The graph has moved left by 5.
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(0, 1). The graph has moved left by 5. (0, 1). The graph has moved left by 5.
Check 8
Why is f(x+2) not a move to the right?
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The curve reaches its old y-values earlier, which is further left. The curve reaches its old y-values earlier, which is further left.
Check 9
Does f(-x) change the y-coordinates of points on the graph?
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No. Each point keeps its height, and its x-coordinate changes sign. No. Each point keeps its height, and its x-coordinate changes sign.
Check 10
The point (0, 4) is the y-intercept of y=f(x). What is the y-intercept of y=f(x)+4?
- (0, 1). The graph has moved left by 5.
- (3, 2). The x-coordinate changes sign.
- 8. Adding outside raises the intercept by 4.
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8. Adding outside raises the intercept by 4. 8. Adding outside raises the intercept by 4.
Check 11
Name the two moves in y=f(x-1)-2.
- (2, -7). Only the height changes sign.
- Right by 1, then down by 2.
- (0, 1). The graph has moved left by 5.
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Right by 1, then down by 2. Right by 1, then down by 2.
Check 12
A translation vector for f(x+2) can be written how?
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Left 2, or the vector (-2, 0). Left 2, or the vector (-2, 0).
Check 13
Why track a single point as well as the sentence "move left"?
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The point check catches a sign error in the x-coordinate. The point check catches a sign error in the x-coordinate.
Check 14
The point (-3, 2) is on y=f(x). Where is it on y=f(-x)?
- Right by 1, then down by 2.
- (3, 2). The x-coordinate changes sign.
- 8. Adding outside raises the intercept by 4.
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(3, 2). The x-coordinate changes sign. (3, 2). The x-coordinate changes sign.
Check 15
Which is vertical: f(x)+2 or f(x+2)?
- (3, 2). The x-coordinate changes sign.
- 8. Adding outside raises the intercept by 4.
- f(x)+2. The change is outside the bracket.
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f(x)+2. The change is outside the bracket. f(x)+2. The change is outside the bracket.
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