graph transformations

Question 1

y = f(x) + a

Answer 1

• translation along vector (0 ⁄ a)
• stays same shape - moves up/down

Question 2

y = f(x + a)

Answer 2

• translation along vector (-a ⁄ 0)
• stays same shape - moves left/right (opposite of what you think)

Question 3

y = -f(x)

Answer 3

• reflection of the graph in the x-axis
• stays same shape - upside down

Question 4

y = f(-x)

Answer 4

• reflection of the graph in the y-axis
• stays same shape - looks back to front

Question 5

y = af(x)

Answer 5

• stretch by a scale factor of a in the y direction
• similar shape but looks stretched (higher than original line)

Question 6

y = f(ax)

Answer 6

• stretch by a scale factor of 1⁄ a in the x direction
• similar shape but looks stretched (lower than original line)