# Lesson Worksheet: Function Transformations: Translations Mathematics

In this worksheet, we will practice identifying function transformations involving horizontal and vertical shifts.

Q1:

Which of the following is the graph of ?  • A(c)
• B(d)
• C(a)
• D(b)

Q2:

The function is translated 2 units in the direction of the positive x-axis. What is the equation of the resulting function?

• A
• B
• C

Q3:

The function is translated eight down. Write, in terms of , the equation of the translated graph.

• A
• B
• C
• D
• E

Q4:

Consider the function .

Which of the following is the graph of ? • AC
• BB
• CA
• DD

State the domain and range of .

• Bdomain: , range:
• Cdomain: , range:
• Ddomain: , range:

Q5:

Consider the root function .

The function has been obtained by translating three units down and five units to the left. Write its equation.

• A
• B
• C
• D
• E

State the domain and range of .

• Bdomain: , range:
• Cdomain: , range:
• Ddomain: , range:
• Edomain: , range:

Q6:

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q7:

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q8:

The figure shows the graph of and point . Point is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q9:

The figure shows the graph of and point , which is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q10:

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q11:

The function is translated four up. Write, in terms of , the equation of the translated graph.

• A
• B
• C
• D
• E

Q12:

Graph (a) shows the curve , which has a point of inflection at the origin. Determine the equation of graph (b), given that it is a translation of graph (a). • A
• B
• C
• D
• E

Q13:

The function is translated three to the right. Write, in terms of , the equation of the translated graph.

• A
• B
• C
• D
• E

Q14:

Let . For any function , what transformation takes the graph of to the graph of ?

• Aa translation right by 4 units
• Ba translation up by 4 units
• Ca translation down by 4 units
• Da translation left by 4 units
• Ea reflection in the line

Q15:

The following is the graph of the function , which takes a real number and returns its fractional part. What are the values of , and ?

• A0, 0.35, 0.67
• B0, 4, 12,345
• C4, 4, 12,345
• D4, 0.35, 0.67
• E0, 0.35, 0.67

What are the values of and ? Be careful, this is not as straightforward as for positive inputs!

• A, 4
• B, 0.65
• C,
• D0.99,
• E0.99, 0.65

The following is the graph of the function . By considering suitable translations, express in terms of .

• A
• B
• C
• D
• E

The following is the graph of the triangle function . Use the absolute value function to express in terms of .

• A
• B
• C
• D
• E

Q16:

The red graph in the figure has equation and the blue graph has equation . Express as a transformation of . • A
• B
• C
• D
• E

Q17:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q18:

Which of the following equations could be that of the given graph? • A
• B
• C
• D
• E

Q19:

Which of the graphs matches the equation ? • AC
• BD
• CA
• DB

Q20:

The curve of the function is the same curve of the function by translation of magnitude 5 units in which direction?

• A
• B
• C
• D

Q21:

The red graph in the figure has the equation and the blue graph has the equation . Express as a transformation of . • A
• B
• C
• D
• E

Q22:

The red graph in the figure has the equation and the blue graph has the equation . Express as a transformation of . • A
• B
• C
• D
• E

Q23:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q24:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q25:

The function is translated five to the left. Write, in terms of , the equation of the translated graph.

• A
• B
• C
• D
• E