Graph transformations: where does the point go?

The Maths Habit

Sam moves the point (3, 2) 4 to the right and gets (3, 6). Is Sam right?

No: moving right changes x, so it is (7, 2)

Up, down, left or right?

y = f(x) + 3 Up 3

Up, down, left or right?

y = f(x − 3) Right 3

Up, down, left or right?

y = f(x + 2) Left 2

Outside the bracket changes y.

Inside the bracket changes x, the opposite way.

(3, 2) is on y = f(x). Where is it on y = f(x) + 4?

outside the bracket changes y; inside changes x, the opposite way
−6−4−2246−4−22468
xy
before
32
after
36
Answer(3, 6)

(1, 4) is on y = f(x). Where is it on y = f(x − 2)?

outside the bracket changes y; inside changes x, the opposite way
−6−4−2246−4−22468
xy
before
14
after
34
Answer(3, 4)

(3, 2) is on y = f(x). Where is it on y = f(x) + 4?

outside the bracket changes y; inside changes x, the opposite way
−6−4−2246−4−22468
xy
before
32
after
36
Answer(3, 6)

(2, 3) is on y = f(x). Where is it on y = −f(x)?

outside the bracket changes y; inside changes x, the opposite way
−6−4−2246−4−22468
xy
before
23
after
2−3
Answer(2, −3)

Graph transformations: where does the point go? worksheet, page 1

Answer sheet

  1. y = f(x) has a minimum point at (3, −2). Find the minimum point of y = f(x − 4) + 1.

    (7, −1)

  2. y = f(x) crosses the y axis at (0, 4). Where does y = −f(x) cross the y axis?

    (0, −4)

  3. (4, −3) is on y = f(x). On a new graph it is at (1, −3). Write the equation of the new graph.

    Left 3: y = f(x + 3)

  1. (4, 1) is on y = f(x). Where is it on y = f(x + 2)?

    (2, 1)

  2. (−3, 2) is on y = f(x). Where is it on y = −f(x)?

    (−3, −2)

  3. (−1, 5) is on y = f(x). On a new graph it is at (3, 5). Write the equation of the new graph.

    y = f(x − 4)
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