Function Notation Graph Translations

Are these two functions inverses of each other?

• Yes, they are inverses of each other

• No, they are not inverses of each other

• They are inverses of each other only for certain values

• Cannot be determined without more information

The placement of a green floor tile among white floor tiles is determined using a translation as shown at the right. Describe the translation from tile 1 to tile 2 using coordinate notation and words. Describe the translation from tile 1 to tile 3 using a translation vector.

• coordinate notation: (x, y) -> (x + 2, y + 3)

  words: The tile is translated 2 tiles right and 3 tiles up. translation vector for tile 1 to tile 3: ⟨4,6⟩

• coordinate notation: (x, y) -> (x - 2, y - 3)

  words: The tile is translated 2 tiles left and 3 tiles down.

  translation vector for tile 1 to tile 3: ⟨2,3⟩

• coordinate notation: (x, y) -> (x - 2, y - 3)

  words: The tile is translated 2 tiles right and 3 tiles up.

  translation vector for tile 1 to tile 3: ⟨2,3⟩

• coordinate notation: (x, y) -> (x + 2, y + 3)

  words: The tile is translated 2 tiles left and 3 tiles down.

  translation vector for tile 1 to tile 3: ⟨4,6⟩

The graph shows repeated translations that result in the animation of the soccer ball. If you follow the pattern, what will be the coordinates of the translation to position 4?

• (5, −3)

• (4, −3)

• (4, −2)

• (5, −2)

Describe the transformation.

• Vertical translation down 1

• Reflection over the y-axis

• Vertical translation up 1

• Reflection over the x-axis

Which of the following equations is the functionof the graph shown?

Describe the transformations.

• Horizontal Translation Right 2, Vertical Translation Down 4

• Horizontal Translation Left 2, Vertical Translation Down 4

• Horizontal Translation Left 2, Vertical Translation Up 4

• Horizontal Translation Right 2, Vertical Translation Up 4

Which function matches the graph?

• f(x) = ∛(x + 3) + 2

• f(x) = − ∛(x - 3) + 2

• f(x) = ∛(x - 3) + 2

• f(x) = ∛(x - 2) + 3

Identify the Transformations. 

• Vertical stretch by 2 and down 4

• Horizontal compression by ½ and down 4

• Vertical stretch by 2 and up 4

• Horizontal compression by ½ and right 4

Which of the following is not true about the function shown?

• The function has been shifted 6 units right.

• The function has been shifted up 1 unit

• The function has been vertically stretched by a factor of 2.

• reflection over the x-axis, horizontal translation left 2

• reflection over the x-axis, vertical translation up 2

• reflection over the x-axis, horizontal translation right 2 

• reflection over the x-axis, vertical translation down 2