Home › Worksheets › A Level Year 12 Math › Graphs and Transformations Prepared by Mohsim Digital Education
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y = f(x) + a shifts f(x) vertically by a and y = f(x + a) shifts it left by a for a > 0, so this Year 12 sheet opens with the two translation rules. The key adds reflections in both axes and a vertical stretch by factor 2.
Key Takeaways
y = f(x) + a is a vertical shift (Q1).
y = f(x + a) shifts left by a (Q2).
Q3 records a reflection in the x-axis.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
The graph of y = f(x) + a is
(a) f(x) shifted vertically by a (b) f(x) shifted horizontally (c) f(x) reflected (d) f(x) stretched
2.
The graph of y = f(x + a), for a > 0, is
(a) f(x) shifted left by a (b) f(x) shifted right by a (c) f(x) stretched vertically (d) f(x) reflected in the x-axis
3.
The graph of y = −f(x) is
(a) f(x) reflected in the x-axis (b) f(x) reflected in the y-axis (c) f(x) stretched (d) f(x) shifted
4.
The graph of y = f(−x) is
(a) f(x) reflected in the y-axis (b) f(x) reflected in the x-axis (c) f(x) shifted (d) f(x) compressed
5.
The graph of y = 2f(x) is
(a) f(x) stretched vertically by a factor of 2 (b) f(x) compressed vertically (c) f(x) shifted up by 2 (d) f(x) reflected
6.
The graph of y = f(2x) is
(a) f(x) compressed horizontally by a factor of 2 (b) f(x) stretched horizontally (c) f(x) shifted (d) f(x) reflected
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
What does the graph y = f(x) + 3 represent?
8.
What does the graph y = f(x − 2) represent?
9.
How do you reflect a graph in the x-axis?
10.
How do you reflect a graph in the y-axis?
11.
What is the effect of y = af(x) when a > 1?
12.
What is the effect of y = f(x/b) when b > 1?
13.
Describe the transformation y = f(x) − 5.
14.
What is the vertex of y = x² after shifting it up by 3?
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
The graph of y = x² is shifted up by 4. Write the new equation.
16.
The graph of y = x² is shifted to the right by 3. Write the new equation.
17.
Reflect the graph of y = x² in the x-axis. Write the new equation.
18.
The graph of y = x² is stretched vertically by a factor of 2. Write the new equation.
19.
The graph of y = f(x) is shifted to the left by 5. Write the new equation.
20.
Reflect the graph of y = x³ in the y-axis. Write the new equation.
Answer Key
1. a) f(x) shifted vertically by a
2. a) f(x) shifted left by a
3. a) f(x) reflected in the x-axis
4. a) f(x) reflected in the y-axis
5. a) f(x) stretched vertically by a factor of 2
6. a) f(x) compressed horizontally by a factor of 2
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What does y = f(x) + a do to the graph?
Shifts f(x) vertically by a, option (a) in this worksheet (Q1).
What does y = f(x + a) do for a > 0?
Shifts f(x) left by a, option (a) in this worksheet (Q2).
How is f(x) reflected in the x-axis written?
Recorded as option (a) in this worksheet (Q3).