Question

1.1 review
state the domain and range of the following functions in
interval notation.
7.
graph of a function with x - axis, y - axis, an open circle at (0,0), and a curve on the left - hand side of the y - axis
domain:
range:

Explanation:

Step1: Analyze the Domain

The domain of a function is the set of all possible x - values for which the function is defined. Looking at the graph, we can see that there is an open circle at \(x = 0\), which means \(x=0\) is not included, and the graph extends to the left (towards negative infinity) and up to but not including \(x = 0\). So the domain is all real numbers less than 0, which in interval notation is \((-\infty,0)\).

Step2: Analyze the Range

The range of a function is the set of all possible y - values the function can take. Looking at the graph, the function seems to take on all real number values (since it goes downwards without bound and also has values that can reach any real number as we move along the x - axis towards negative infinity). So the range is all real numbers, which in interval notation is \((-\infty,\infty)\) or \(\mathbb{R}\).

Answer:

Domain: \((-\infty, 0)\)
Range: \((-\infty, \infty)\)