# Lesson Worksheet: Combining Function Transformations Mathematics

In this worksheet, we will practice identifying function transformations that include a combination of translation, dilation, and reflection.

Q1:

The following graph represents a function after a reflection on the and a horizontal dilation by a scale factor of . Which of the following represents the original function ? • A
• B
• C
• D
• E

Q2:

The function is reflected in the and then shifted 3 units in the positive -direction. Write the equation of the transformed function .

• A
• B
• C
• D
• E

Q3:

The following graph represents a function . Find the resulting function after a reflection on the followed by a translation by 2 units in the positive direction of the . • A
• B
• C
• D
• E

Q4:

Which of the following processes would you use to obtain the graph of from the graph of ?

1. reflect the graph in the -axis
2. reflect the graph in the -axis
3. stretch the graph in the horizontal direction by a factor of 3
4. stretch the graph in the horizontal direction by a factor of
• Ac and d
• Bb and d
• Ca and c
• Da and d
• Eb and c

Q5:

If the following graph is reflected in the -axis and then shifted to the left by 1 unit and down by 3 units, what is the equation of the new graph? • A
• B
• C
• D

Q6:

The function is stretched in the vertical direction by a scale factor of 2 then reflected in the . Write the equation of the transformed function .

• A
• B
• C
• D
• E

Q7:

The graph of the function is first reflected symmetrically over the axis, then shifted up 2 units and right by 3, and finally horizontally stretched by 2 to obtain the graph of the function . Write an equation for .

• A
• B
• C
• D
• E

Q8:

This is the graph of the exponential function . Which of the following is the graph of ?  • A(a)
• B(b)
• C(c)

Q9:

The graph represents a function after a vertical positive shift by 3 units followed by a reflection on the . Which of the following represents the original function ? • A
• B
• C
• D
• E

Q10:

The red graph in the figure has the equation and the blue graph has the equation . Which of the following will not transform the graph of onto the graph of ? • AA reflection in the , followed by a horizontal shift of 4 units to the left
• BA vertical shift of 4 units down, followed by a reflection in the
• CA horizontal shift of 4 units to the right, followed by a reflection in the
• DA reflection in the

This lesson includes 29 additional questions and 189 additional question variations for subscribers.