Question

Graph each absolute value function. State the domain, range, and y-intercept.

Answer 1

Domain : all real numbers.

Y-intercept : (0,-1)

The range is y >= -3.

Explanation:

We have given the function:

y = 2Ix-1I -3

We have to draw the graph of this equation.

As see from the equation the domain is :

domain: all real numbers.

As we see from the graph the y-intercept is -1 (the point where x = 0)

y-intercept = (0,-1)

The range is y >= -3.

The graph is attached with the question.

Answer 2

The domain ⇒ x ∈ real number

The range ⇒ y ≥ -3

The y-intercept ⇒ (0 , -1)

Explanation:

∵ y = 2Ix - 1I - 3

∴ y = 2(x - 1) - 3

∴ y = 2x - 2 - 3 = 2x - 5 ⇒ positive slope

∴ y = 2(-x + 1) - 3

∴ y = -2x + 2 - 3 = -2x - 1 ⇒ negative slope

∴ 2x - 5 = -2x - 1 ⇒ 4x = 4 ⇒ x = 1

∴ Y = 2(1) - 5 = -3

∴ The two lines intersect each other at (1 , -3)

∴ The domain is x ∈ real number

∴ The range is y ≥ -3

∴ The y-intercept = -1 ⇒ (0 , -1)