Grade 9 · Math · Algebra 1

9th grade Graph absolute value, square root and cube root functions worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Graph absolute value, square root and cube root functions

Grade 9 Math Worksheet

NameDate

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

1.
Bo graphs y = |x + 6| − 2 for a tent roof drawing. What is the range?
- y ≥ -6
- All real numbers
- y ≥ -2
2.
Esme graphs y = 3|x − 2| + 7 for a castle gate arch in a game. What is the range?
Use the picture in question 1.
- y ≥ 2
- All real numbers
- y ≥ 7
3.
Kira graphs y = √(x + 3) − 2 for a water slide model. What is the domain?
- y ≥ -2
- x ≥ -3
- All real numbers
- x ≥ 3
4.
Milo graphs y = √(x + 1) + 6 for a cart track. What is the domain?
Use the picture in question 3.
- x ≥ 1
- y ≥ 6
- x ≥ -1
- All real numbers
5.
Noah graphs y = √(x − 5) − 4 for a toy train hill. What is the domain?
Use the picture in question 3.
- x ≥ 5
- All real numbers
- y ≥ -4
- x ≥ -5
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?
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?
Zee designs a V-shaped ramp for a rolling play ball. On the grid, the vertex is (-2, 3) and the ramp passes through (0, 11). What is the slope of the right side?
9.
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 − 4| − 3
- y = |x − 3| + 4
10.
Bo slides the graph of y = |x| so its vertex lands on (5, -2) for a crown design. Which equation is the new graph?
Use the picture in question 9.
- y = |x + 2| + 5
- y = |x + 5| − 2
- y = |x − 5| − 2

9th grade Graph absolute value, square root and cube root functions worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Graph absolute value, square root and cube root functions. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the vertex of y = |x − 3| + 2 and the start point of y = √(x + 1) − 4 from the equation.
I can give the domain and range, and the slope of each side of a V.
I can move a point of y = |x| through a flip, a stretch and a shift, and pick the equation of a V from its graph.

Standard: F-IF.C.7b, F-BF.B.3, F-IF.B.5

Words to know

vertex: The tip of a V, where the graph turns.

start point: Where a square root graph begins; nothing is drawn to its left.

domain: Every input (x-value) the graph uses.

range: Every output (y-value) the graph reaches.

stretch: Multiplying every output by the same number; the V gets steeper.

Common mistakes

Your child moved the graph the wrong way left or right. In y = |x − 3| the graph moves right 3, because x = 3 makes the inside 0.

Your child swapped the left-right move and the up-down move.

Your child said every number works, but this graph has a lowest point or a starting point.

What to say

Ask: which x-value makes the inside 0?

Ask: which number is inside the bars or the root (it moves left or right), and which is outside (it moves up or down)?

Ask: is there a value the graph never goes past?

Questions parents ask

What is the most common mistake with graph absolute value, square root and cube root functions?

Your child moved the graph the wrong way left or right. In y = |x − 3| the graph moves right 3, because x = 3 makes the inside 0.

How can I help my child with graph absolute value, square root and cube root functions?

Ask: which x-value makes the inside 0?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

See all Algebra 1

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records