Shifts, flips and stretches of a function

Answer Key - Grade 9 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Luz marks (-1, 4) on f, a hill on a game map. The new graph is g(x) = f(x + 2) − 3. Which point is on g? Write it like (7, -3).

   (-3, 1)
2. 2.

   Ren flips f for a mirror puzzle. (3, -2) is on f, and g(x) = −f(x). Which point is on g? Write it like (7, -3).

   (3, 2)
3. 3.

   Tala flips f for a butterfly-wing drawing. (-4, 5) is on f, and g(x) = −f(x). Which point is on g? Write it like (7, -3).

   (-4, -5)
4. 4.

   Bo stretches f for a taller slide drawing. (-3, 4) is on f, and g(x) = 2f(x). Which point is on g? Write it like (7, -3).

   (-3, 8)
5. 5.

   Jun stretches f for a tent roof sketch. (-1, -3) is on f, and g(x) = 4f(x). Which point is on g? Write it like (7, -3).

   (-1, -12)
6. 6.

   Kira squashes f for a flatter umbrella top. (-6, 10) is on f, and g(x) = (1/2)f(x). Which point is on g? Write it like (7, -3).

   (-6, 5)

7. Read this first

   Use this

   Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of f is drawn; g is not drawn.

8. 7.

   Luz slides f 4 units left and 1 unit up for a new castle level. Which rule gives the new graph g?

   • g(x) = f(x − 4) + 1
   • g(x) = f(x + 1) + 4
   • g(x) = f(x + 4) + 1
9. 8.

   Milo slides f 2 units right and 5 units down for a river level. Which rule gives the new graph g?

   • g(x) = f(x + 2) − 5
   • g(x) = f(x − 2) − 5
   • g(x) = f(x − 5) − 2
10. 9.

    Noah slides f 3 units left and 6 units down for a snow level. Which rule gives the new graph g?

    • g(x) = f(x + 3) − 6
    • g(x) = f(x + 6) − 3
    • g(x) = f(x − 3) − 6
11. 10.

    Pia slides f 6 units right and 2 units up for a windy level. Which rule gives the new graph g?

    • g(x) = f(x − 6) + 2
    • g(x) = f(x − 2) + 6
    • g(x) = f(x + 6) + 2