Shifts, flips and stretches of a function

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 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.

2. 1.

   Luz has the graph of f(x) = |x| in a drawing app. The new graph is g(x) = f(x − 5). How does the graph of f move to make g?

   • 5 units left
   • 5 units down
   • 5 units right
3. 2.

   Milo has the graph of f(x) = x² on the class screen. The new graph is g(x) = f(x) + 2. How does the graph of f move to make g?

   • 2 units down
   • 2 units right
   • 2 units up
4. 3.

   Noah has the graph of f(x) = x² on graph paper. The new graph is g(x) = f(x + 3). How does the graph of f move to make g?

   • 3 units up
   • 3 units right
   • 3 units left
5. 4.

   Pia has the graph of f(x) = |x| for a robot's path in a game. The new graph is g(x) = f(x) − 4. How does the graph of f move to make g?

   • 4 units left
   • 4 units down
   • 4 units up
6. 5.

   Tala moves f(x) = |x| to g(x) = f(x) + 3 for a castle wall in a game. One row is done. Where does (-2, 2) go? Write it like (7, -3).

   (-2, 5)
7. 6.

   Zee moves f(x) = |x| to g(x) = f(x + 2) for a kite's flight path. One row is done. Where does (-3, 3) go? Write it like (7, -3).

   (-5, 3)

8. Table for f

   x	f(x)
   2	5

9. 7.

   Bo has a table for f, the graph of a bouncing play ball in a game. It shows f(2) = 5. A new function is g(x) = 3f(x). What is g(2)?

   15
10. 8.

    Esme has a table for f, the graph of a rocket's climb. It shows f(-3) = 6. A new function is g(x) = 2f(x). What is g(-3)?

    12
11. 9.

    Jun has a table for f, the graph of a wave under a toy boat. It shows f(6) = -2. A new function is g(x) = 4f(x). What is g(6)?

    -8
12. 10.

    Kira has a table for f, the graph of a kite's height. It shows f(-1) = 7. A new function is g(x) = 5f(x). What is g(-1)?

    35