Graph transformations: translations

The Maths Habit Handout to print

A shape on a grid slides 3 squares to the right. What happens to the coordinates of every corner?

Each x goes up by 3. Each y stays the same.

Transformation
A change to a graph: a slide, a flip or a stretch.
Translation
A slide. Every point moves the same distance in the same direction.

f(x) + 2up 2 f(x) − 2down 2 f(x + 2)left 2 f(x − 2)right 2

Sketch
y = f(x) − 2

Sketch y = f(x) + 3.

The graph moves
updownleftright
by3squares
P goes to (1,1)

Sketch y = f(x) − 2.

The graph moves
updownleftright
by2squares
P goes to (1,−4)

Sketch y = f(x) + 3.

The graph moves
updownleftright
by3squares
P goes to (1,1)

Sketch y = f(x) + 2.

The graph moves
updownleftright
by2squares
P goes to (1,0)

Which way does the graph move?

y = f(x − 4) Right 4

Sketch y = f(x + 3).

The graph moves
updownleftright
by3squares
P goes to (−2,−2)

Sketch y = f(x − 3).

The graph moves
updownleftright
by3squares
P goes to (4,−2)

Sketch y = f(x + 3).

The graph moves
updownleftright
by3squares
P goes to (−2,−2)

Sketch y = f(x + 4).

The graph moves
updownleftright
by4squares
P goes to (−3,−2)

Graph transformations worksheet, page 1

Graph transformations worksheet, page 2

Answer sheet

  1. The graph of y = f(x) has a turning point at (2, −5). The graph of y = f(x + a) + b has its turning point at (−1, 0). Find a and b.

    a = 3, b = 5

  2. The graph of y = x2 is moved 4 right and 1 up. Write its new equation.

    y = (x − 4)2 + 1

  1. P(4, −1) is on y = f(x). Where is P on y = f(x) + 5?

    (4, 4)

  2. The graph of y = f(x) is drawn. Sketch y = f(x + 2).

    Moved 2 left
    xy−4−3−2−101234−101234

  3. The graph of y = x2 is moved 3 left and 2 down. Write its new equation.

    y = (x + 3)2 − 2
Exit tickets to print