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.

   Milo marks (2, 3) on f, a bike trail in a game. The new graph is g(x) = f(x − 5) + 1. Which point is on g? Write it like (7, -3).

   (7, 4)
3. 3.

   Noah marks (-3, -2) on f, a toy train track. The new graph is g(x) = f(x − 1) + 6. Which point is on g? Write it like (7, -3).

   (-2, 4)
4. 4.

   Pia marks (4, -1) on f, a star's path in a game sky. The new graph is g(x) = f(x + 4) + 2. Which point is on g? Write it like (7, -3).

   (0, 1)
5. 5.

   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)
6. 6.

   Zee flips f for a leaf pattern. (2, 6) is on f, and g(x) = f(−x). Which point is on g? Write it like (7, -3).

   (-2, 6)
7. 7.

   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)

8. 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.

9. 8.

   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
10. 9.

    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 − 5) − 2
    • g(x) = f(x + 2) − 5
    • g(x) = f(x − 2) − 5
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