# 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 This lesson includes 70 additional question variations for subscribers.