Question

1. Create a table of values and sketch a graph of the piecewise function.

2. Be sure to use the correct notation to indicate any start/end points on your graph.
3. Label your x and y axis with your increments.
4. Identify the domain and range using interval notation.

f(x)=2x-1 when x<1
f(x)=x+1 when x≥1

Answer 1

Piecewise function graph with domain (-∞, 1) ∪ (1, ∞) and range [-3, ∞) is continuous, increasing, and starts/ends at x=1 (open circles).

Create a table of values and sketch a graph of the piecewise function.

Table of values:

x f(x)

-1 -3

0 -1

1 0

2 3

3 4

Sketch of the graph:

Image of piecewise function graphOpens in a new window

Use the correct notation to indicate any start/end points on your graph.

The start/end point of the first piece is at x = 1, and the start/end point of the second piece is also at x = 1. We will use open circles to indicate these points, since the function is not defined at x = 1.

Label your r2 and y axis with your increments.

The x-axis is labeled with increments of 1, and the y-axis is labeled with increments of 2.

Identify the domain and range using interval notation.

The domain of the function is all real numbers except for x = 1, which we can write in interval notation as:

(-∞, 1) \cup (1, ∞)

The range of the function is all real numbers greater than or equal to -3, which we can write in interval notation as:

[-3, ∞]