Graph absolute value, square root and cube root functions

Answer Key - Grade 9 Math Worksheet

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

2. 1.

   Bo graphs y = |x + 6| − 2 for a tent roof drawing. What is the range?

   • All real numbers
   • y ≥ -2
   • y ≥ -6
3. 2.

   Jun graphs y = 2|x + 5| + 3 for a ladder-and-slide drawing. What is the range?

   Use the picture in question 1.

   • y ≥ -5
   • All real numbers
   • y ≥ 3
5. 3.

   Kira graphs y = √(x + 3) − 2 for a water slide model. What is the domain?

   • x ≥ -3
   • y ≥ -2
   • x ≥ 3
   • All real numbers
6. 4.

   Noah graphs y = √(x − 5) − 4 for a toy train hill. What is the domain?

   Use the picture in question 3.

   • x ≥ -5
   • y ≥ -4
   • All real numbers
   • x ≥ 5
7. 5.

   Pia designs a V-shaped ramp for a toy car. On the grid, the vertex is (2, 1) and the ramp passes through (0, 7). What is the slope of the left side?

   -3
8. 6.

   Ren designs a V-shaped ramp for a bike jump. On the grid, the vertex is (-3, -5) and the ramp passes through (1, 3). What is the slope of the right side?

   2
9. 7.

   Tala designs a V-shaped ramp for a scooter. On the grid, the vertex is (1, 2) and the ramp passes through (-3, 4). What is the slope of the left side?

   -1/2
11. 8.

    Ari slides the graph of y = |x| so its vertex lands on (-3, 4) for a star-catching game level. Which equation is the new graph?

    • y = |x + 3| + 4
    • y = |x − 3| + 4
    • y = |x − 4| − 3
12. 9.

    Esme slides the graph of y = |x| so its vertex lands on (-2, -6) for an umbrella pattern. Which equation is the new graph?

    Use the picture in question 8.

    • y = |x + 6| − 2
    • y = |x − 2| − 6
    • y = |x + 2| − 6
13. 10.

    Jun slides the graph of y = |x| so its vertex lands on (1, 3) for a magnet maze level. Which equation is the new graph?

    Use the picture in question 8.

    • y = |x + 1| + 3
    • y = |x − 3| + 1
    • y = |x − 1| + 3