Question

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The absolute value function can be defined using piecewise notation.

A(x)=x , x ≥ 0

A(x)=−x , x < 0

Use this notation to find the following values:

1. A(10) = (answer)

2. A(0) = (answer)

3. A(−3)= (answer)

4. A(3.14159)= (answer)

5. A ( x ) = 7; x= (answer) and x= (answer)

Answer 1

The values of A(x) for different x values using the absolute value function in piecewise notation.

Step-by-step explanation:

1. A(10) = 10, since 10 is greater than or equal to 0.
2. A(0) = 0, since 0 is equal to 0.
3. A(-3) = -(-3) = 3, since -3 is less than 0 and the absolute value of -3 is 3.
4. A(3.14159) = 3.14159, since 3.14159 is greater than or equal to 0.
5. A(x) = 7 has no solution, since the absolute value function is not equal to a constant for any x value.

Answer 2

A(10) = 10

A(0) = 0

A(−3) = -3

A(3.14159) = 3.14159

A( x ) = 7 , x = 7

A(10) = -10

A(0) = 0

A(−3) = 3

A(3.14159) = -3.14159

A( x ) = 7 , x = -7

Step-by-step explanation:

Given:

A(x)=x , x ≥ 0

A(x)=−x , x < 0

Find:

A(10) =

A(0) =

A(−3) =

A(3.14159) =

A( x ) = 7

Computation:

A(x)=x;

A(10) = 10

A(0) = 0

A(−3) = -3

A(3.14159) = 3.14159

A( x ) = 7 , x = 7

A(x)=−x;

A(10) = -10

A(0) = 0

A(−3) = 3

A(3.14159) = -3.14159

A( x ) = 7 , x = -7