Transformations of Graphs in Words

Recall transformations from our functions unit where we can shift graphs up, down, left, and right, or we can make graphs steeper and narrower with vertical and horizontal stretches and compressions. What does letter A do in the equation below? y=A\sin\left(B\left(x-h\right)\right)+k

• Stretches or compresses the graph vertically (aka affects the amplitude)

• Stretches or compresses the graph horizontally (aka affects the period)

• Shifts the graph left or right

• Shifts the graph up or down

Recall transformations from our functions unit where we can shift graphs up, down, left, and right, or we can make graphs steeper and narrower with vertical and horizontal stretches and compressions. What does letter h do in the equation below? y=A\sin\left(B\left(x-h\right)\right)+k

• Stretches or compresses the graph vertically (aka affects the amplitude)

• Stretches or compresses the graph horizontally (aka affects the period)

• Shifts the graph left or right

• Shifts the graph up or down

Recall transformations from our functions unit where we can shift graphs up, down, left, and right, or we can make graphs steeper and narrower with vertical and horizontal stretches and compressions. What does letter B do in the equation below?

• Stretches or compresses the graph vertically (aka affects the amplitude)

• Stretches or compresses the graph horizontally (aka affects the period)

• Shifts the graph left or right

• Shifts the graph up or down

• Stretches or compresses the graph vertically (aka affects the amplitude)

• Stretches or compresses the graph horizontally (aka affects the period)

• Shifts the graph left or right

• Shifts the graph up or down

• Horizontal translation left 16
• Horizontal translation right 16
• Vertical translation down 16
• Vertical translation up 16

• Horizontal translation right 2; Vertical translation down 12
• Horizontal translation right 2; Vertical translation down 4
• Horizontal translation left 2; vertical translation down 12
• Horizontal translation left 2; vertical translation down 4

How did this graph move from the parent function?

• Up 2, Reflected over x-axis, and Right 4

• Up 2, Reflected over x-axis, and Left 4

• Reflected over x-axis, Down 4, and Right 2

• Reflected over x-axis, Up 4, and Left 2

What are the transformations of this function compared to the parent function?

• Translated down 2

• Translated up 2

• Translated left 2

• Translated right 2

What are the transformations of this functions compared to the parent function?

• Shifted down 2

• Shifted up 2

• Shifted left 2

• Shifted right 2

Describe the transformation.

• Left 1 unit, Reflect over x-axis, Up 2 units

• Left 1 unit, Reflect over y-axis, Down 2 units

• Right 1 unit, Reflect over x-axis, Up 2 units

• Right 1 unit, Reflect over y-axis, Up 2 units