Understanding the sgn(x) Function

What is the value of sgn(5)?

• 5

• -1

• 1

• 0

What is the value of sgn(-3)?

• 0

• 1

• -1

• 3

What is the value of sgn(0)?

• 0

• 1

• -1

• undefined

Graph the sgn(x) function for x values from -5 to 5.

• The graph of sgn(x) is a continuous curve that smoothly transitions between -1 and 1.

• The graph of sgn(x) is a step function with values -1 for x < 0, 0 at x = 0, and 1 for x > 0.

• The graph of sgn(x) is a parabolic function opening upwards.

• The graph of sgn(x) is a linear function with a slope of 1.

Identify the piecewise definition of sgn(x).

• sgn(x) = { -1 if x > 0, 0 if x < 0, 1 if x = 0 }

• sgn(x) = { -1 if x < 0, 0 if x = 0, 1 if x > 0 }

• sgn(x) = { 1 if x < 0, 0 if x = 0, -1 if x > 0 }

• sgn(x) = { 0 if x < 0, 1 if x = 0, -1 if x > 0 }

Evaluate sgn(-10) + sgn(10). What is the result?

• 1

• -1

• 0

• 10

If x < 0, what is sgn(x)?

• 0

• 1

• 2

• -1

If x > 0, what is sgn(x)?

• undefined

• 0

• 1

• -1

If x = 0, what is sgn(x)?

• 1

• 0

• undefined

• -1

Solve the inequality sgn(x) > 0.

• x > 0

• x ≤ 0

• x < 0

• x = 0