write the domain and range of each graph using interval notation.

Explanation:

Step1: Recall domain and range definitions

Domain is set of all x - values, range is set of all y - values.

Step2: Analyze graph 1

The line extends infinitely in both x and y directions. Domain: $(-\infty,\infty)$, Range: $(-\infty,\infty)$.

Step3: Analyze graph 2

The x - values extend infinitely in both directions, and y - values have a minimum. Domain: $(-\infty,\infty)$, Range: $[y_{min},\infty)$ (where $y_{min}$ is the y - coordinate of the lowest point on the graph).

Step4: Analyze graph 3

The x - values extend infinitely in both directions, and y - values have a minimum. Domain: $(-\infty,\infty)$, Range: $[y_{min},\infty)$ (where $y_{min}$ is the y - coordinate of the lowest point on the graph).

Step5: Analyze graph 4

The graph is a horizontal line. x - values extend infinitely, y is a constant. Domain: $(-\infty,\infty)$, Range: ${y_{constant}}$.

Step6: Analyze graph 5

The parabola opens upwards. x - values extend infinitely, y has a minimum at the vertex. Domain: $(-\infty,\infty)$, Range: $[0,\infty)$ (assuming vertex is at origin).

Step7: Analyze graph 6

The x - values extend infinitely in both directions, and y - values extend infinitely downwards and have an upper - bound. Domain: $(-\infty,\infty)$, Range: $(-\infty,y_{max}]$ (where $y_{max}$ is the y - coordinate of the highest point on the graph).

Answer:

1. Domain: $(-\infty,\infty)$, Range: $(-\infty,\infty)$
2. Domain: $(-\infty,\infty)$, Range: $[y_{min},\infty)$
3. Domain: $(-\infty,\infty)$, Range: $[y_{min},\infty)$
4. Domain: $(-\infty,\infty)$, Range: ${y_{constant}}$
5. Domain: $(-\infty,\infty)$, Range: $[0,\infty)$
6. Domain: $(-\infty,\infty)$, Range: $(-\infty,y_{max}]$