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# Lesson Worksheet: Solving Absolute Value Problems Mathematics

In this worksheet, we will practice solving equations involving absolute values algebraically and graphically.

**Q1: **

Given the function , , solve the equation .

- A or
- B or
- C or
- D or
- E or

**Q2: **

Which of the following graphs represents ?

- A
- B
- C
- D
- E

Find its domain and range.

- AThe domain is , and the range is .
- BThe domain is , and the range is .
- CThe domain is , and the range is .
- DThe domain is , and the range is .
- EThe domain is , and the range is .

**Q3: **

Which of the following functions is represented by the given graph?

- A
- B
- C
- D
- E

Find its domain and range.

- AThe domain is , and the range is .
- BThe domain is , and the range is .
- CThe domain is , and the range is .
- DThe domain is , and the range is .
- EThe domain is , and the range is .

**Q4: **

Find the range of the function .

- A
- B
- C
- D
- E

**Q5: **

Find the domain and range of the function .

- AThe domain is and the range is .
- BThe domain is and the range is .
- CThe domain is and the range is .
- DThe domain is and the range is .

**Q6: **

The graph in figure (i) is of , which could also be written as follows

Find the values of and that would make graph (ii) that of .

- A
- B
- C
- D
- E

**Q7: **

The equations and are defined by where is a constant.

The equation has exactly one real root. Find the value of .

**Q8: **

A function is defined by . A sketch of the graph of this function is shown below.

Why does **not** exist?

- A is a one-to-one function.
- B is not a straight line.
- C is a many-to-one function.
- D is a one-to-many function.
- E is not defined for all values of .

Solve the inequality .

- A
- B
- C
- D
- E

**Q9: **

The function is defined as , . Which of the following sketches is correctly shaded to represent the region that satisfies ?

- A
- B
- C
- D
- E