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.

   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)
2. 2.

   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)
3. 3.

   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)
4. 4.

   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)
5. 5.

   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)
6. 6.

   Ari flips f for a snowflake design. (-5, -1) is on f, and g(x) = f(−x). Which point is on g? Write it like (7, -3).

   (5, -1)
7. 7.

   Esme stretches f for a rocket path in a game. (5, -2) is on f, and g(x) = 3f(x). Which point is on g? Write it like (7, -3).

   (5, -6)
8. 8.

   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)

9. 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.

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 − 2) − 5
    • g(x) = f(x − 5) − 2
    • g(x) = f(x + 2) − 5
11. 10.

    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 + 3) − 6
    • g(x) = f(x + 6) − 3