Questions: Decide whether the relation defined by the graph to the right defines a function, and give the domain and range. Determine the domain. The domain is [0, ∞). The range is the set of all the y-values of the points on the graph. Now determine the range. The range is

Solution Steps

To determine if a graph defines a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). This is typically done using the vertical line test. For the domain, we identify all possible x-values the graph covers. For the range, we identify all possible y-values the graph covers. Given the graph extends indefinitely to the right and up and down, the domain is $[0, \infty)$ and the range is $(-\infty, \infty)$.

To determine if the graph represents a function, we apply the vertical line test. This test checks if any vertical line drawn through the graph intersects it at more than one point. If it does not, then the graph represents a function. Given the points \((0, 1)\), \((1, 2)\), and \((2, 3)\), each \(x\)-value corresponds to exactly one \(y\)-value. Therefore, the graph represents a function.

The domain of a function is the set of all possible \(x\)-values. From the given points, the smallest \(x\)-value is 0, and the graph extends indefinitely to the right. Therefore, the domain is \([0, \infty)\).

The range of a function is the set of all possible \(y\)-values. The graph extends indefinitely up and down, covering all possible \(y\)-values. Therefore, the range is \((-\infty, \infty)\).

Final Answer