Question

A piecewise function is represented by the graph below.

On a coordinate plane, a piecewise function has 2 lines. The first line is made up of 2 lines. One line goes from (negative 5, 3) to (negative 1, negative 1) and then goes up to a closed circle at (1, 1). The second line has an open circle at (1, 2) and then continues up through (3, 4).
What is the domain for the piece of the function represented by f(x) = x + 1?

x < –1
–1 ≤ x ≤ 1
1 ≤ x < 2
x > 1

Answer 1

The domain for this portion of the function is all real numbers greater than 1.

The domain for the piece of the function represented by ( f(x) = x + 1 ) is ( x > 1 ).

This is because the function ( f(x) = x + 1 ) is defined for all real numbers, and the portion of the piecewise function that corresponds to this function is the line that goes from the closed circle at (1, 1) to the open circle at (1, 2), and then continues up through (3, 4).

Therefore, the domain for this portion of the function is all real numbers greater than 1.