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

f(x) = x + 1 is -1 ≤ x ≤ 1.

Explanation:

Based on the given graph, we can determine the domain for the piece of the function represented by f(x) = x + 1.

The graph consists of two parts: a line segment from (x=-5, y=3) to (x=-1, y=-1), and then another line segment from (x=-1, y=-1) to (x=1, y=1).

For the segment represented by f(x) = x + 1, we are interested in the x-values for which this equation is defined. Looking at the graph, we can see that this line segment lies within the interval -1 ≤ x ≤ 1.

Therefore, the domain for the piece of the function represented by f(x) = x + 1 is -1 ≤ x ≤ 1.