Shifts, flips and stretches of a function

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Ren changes f to g(x) = −f(x − 3) + 2 for a cloud's path in a game. The point (2, 4) is on f. Which point is on g? Write it like (7, -3).

   (5, -2)
2. 2.

   Tala changes f to g(x) = 2f(x + 4) − 5 for a play ball's bounce. The point (-1, 3) is on f. Which point is on g? Write it like (7, -3).

   (-5, 1)
3. 3.

   Ari changes f to g(x) = −2f(x + 2) − 4 for a bike jump. The point (-3, -1) is on f. Which point is on g? Write it like (7, -3).

   (-5, -2)
4. 4.

   (1, 3) | (-3, 3); (2, 5) | (-2, 5); (3, 7) | (-1, 7). Bo slides f(x) = 2x + 1, a train track, sideways for a game. The table shows three points before and after. If g(x) = f(x + c), what is c?

   4
5. 5.

   (-1, 1) | (4, 1); (1, 1) | (6, 1); (2, 4) | (7, 4). Esme slides f(x) = x², a swing path, sideways for a game. The table shows three points before and after. If g(x) = f(x − c), what is c?

   5
6. 6.

   (-2, 2) | (-9, 2); (1, 1) | (-6, 1); (3, 3) | (-4, 3). Jun slides f(x) = |x|, a valley on a map, sideways for a game. The table shows three points before and after. If g(x) = f(x + c), what is c?

   7
7. 7.

   (1, 1) | (7, 1); (2, 4) | (8, 4); (3, 7) | (9, 7). Kira slides f(x) = 3x − 2, a scooter ramp, sideways for a game. The table shows three points before and after. If g(x) = f(x − c), what is c?

   6

8. Read this first

   Use this

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

9. 8.

   Milo shifts a straight bike path. f(x) = 3x − 4 and g(x) = f(x + 2). What is g(x), with one x-term and one number?

   3x + 2
10. 9.

    Noah shifts a ruler line on the screen. f(x) = −2x + 3 and g(x) = f(x − 1). What is g(x), with one x-term and one number?

    -2x + 5
11. 10.

    Pia shifts a rocket's straight climb. f(x) = 4x − 1 and g(x) = f(x + 3). What is g(x), with one x-term and one number?

    4x + 11