Graph absolute value, square root and cube root functions
Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.
Ari moves y = |x| to y = |x − 3| + 1 for a robot jump. The vertex row is done. Where does (2, 2) land? Write it like (7, -3).
Bo moves y = |x| to y = |x + 2| + 4 for a sled ramp in a game. The vertex row is done. Where does (1, 1) land? Write it like (7, -3).
Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = |x| is drawn; the new graph is not. Table old (x, y) | new (x, y): (0, 0) | (-2, 4); (1, 1) | ? Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = |x| is drawn; the new graph is not. Table old (x, y) | new (x, y): (0, 0) | (-2, 4); (1, 1) | ? Coordinate grid −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 y = |x| Table old (x, y) new (x, y) (0, 0) (-2, 4) (1, 1) ? Esme moves y = |x| to y = |x − 5| − 3 for a kite's dip in a game. The vertex row is done. Where does (-1, 1) land? Write it like (7, -3).
Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = |x| is drawn; the new graph is not. Table old (x, y) | new (x, y): (0, 0) | (5, -3); (-1, 1) | ? Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = |x| is drawn; the new graph is not. Table old (x, y) | new (x, y): (0, 0) | (5, -3); (-1, 1) | ? −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 old (x, y) new (x, y) (0, 0) (5, -3) (-1, 1) ? Jun moves y = |x| to y = |x + 4| − 1 for a scooter ramp in a game. The vertex row is done. Where does (3, 3) land? Write it like (7, -3).
Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = |x| is drawn; the new graph is not. Table old (x, y) | new (x, y): (0, 0) | (-4, -1); (3, 3) | ? Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = |x| is drawn; the new graph is not. Table old (x, y) | new (x, y): (0, 0) | (-4, -1); (3, 3) | ? Coordinate grid −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 y = |x| Table old (x, y) | new (x, y) old (x, y) new (x, y) (0, 0) (-4, -1) (3, 3) ? Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = |x| is drawn with its vertex (0, 0); the new graph is not drawn. Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = |x| is drawn with its vertex (0, 0); the new graph is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 y = |x| The new graph is not drawn. Kira graphs y = |x + 4| − 2 on a phone graph app (the app hums while it plots). Where is the vertex? Write it like (7, -3).
Luz graphs y = |x − 6| + 1 on graph paper with a fresh pencil. Where is the vertex? Write it like (7, -3).
Use the picture in question 5.
Milo graphs y = |x + 1| + 3 on the big classroom screen. Where is the vertex? Write it like (7, -3).
Use the picture in question 5.
Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = √x is drawn through (0, 0), (1, 1), (4, 2) and (9, 3); the new graph is not drawn. Coordinate grid, all four quadrants, each square one unit, -10 to 10 on both axes. The graph of y = √x is drawn through (0, 0), (1, 1), (4, 2) and (9, 3); the new graph is not drawn. −10 −8 −6 −4 −2 2 4 6 8 10 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 y = √x The new graph is not drawn. Pia sketches y = √(x − 2) + 5 for a playground slide model. Where does the graph start? Write it like (7, -3).
Ren sketches y = √(x + 3) + 1 for a boat ramp drawing. Where does the graph start? Write it like (7, -3).
Use the picture in question 8.
Zee sketches y = √(x + 6) − 4 for a bike path sketch. Where does the graph start? Write it like (7, -3).
Use the picture in question 8.