Question

7)
domain :
range :

Explanation:

Step1: Determine 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, the leftmost point (the open circle) is at \(x = 3\), and the graph extends to the right (towards positive infinity). Since the point at \(x = 3\) is an open circle, \(x = 3\) is not included, but all values greater than 3 are included. So the domain is \(x>3\) or in interval notation \((3,\infty)\).

Step2: Determine the range

The range of a function is the set of all possible y - values the function can take. Looking at the graph, the lowest y - value (starting from the open circle) has a y - coordinate of 4 (but since the circle is open, 4 is not included? Wait, no, looking at the graph, the open circle is at \((3,4)\), but the graph starts from that open circle and goes up. Wait, actually, when we look at the y - values, the graph starts from the open circle at \(y = 4\) (but since it's an open circle, is 4 included? Wait, no, the open circle means the point \((3,4)\) is not included, but the graph starts just above? Wait, no, looking at the graph, the curve starts at the open circle at \(x = 3\), \(y = 4\) (open circle, so \(x = 3\) is not in domain, but for range, the y - values start from just above 4? Wait, no, actually, when we look at the graph, the y - values of the function start from 4 (but the point \((3,4)\) is not included, but the graph is increasing from there. Wait, no, maybe I misread. Let's check the graph again. The open circle is at \((3,4)\), and the graph goes up from there. So the smallest y - value the function can take is greater than 4? Wait, no, maybe the open circle is at \((3,4)\), but the graph is defined for \(x>3\), and as \(x\) increases, \(y\) increases. So the range is all y - values greater than 4? Wait, no, looking at the graph, when \(x = 3\), the open circle is at \(y = 4\), but the graph starts from that open circle and goes up. Wait, maybe the open circle is a typo, or maybe I misinterpret. Wait, actually, in the graph, the curve starts at the open circle (which is at \(x = 3\), \(y = 4\)) and then increases. So the domain is \(x>3\) (since the open circle at \(x = 3\) means \(x = 3\) is not included, and the graph goes to the right), and the range is \(y>4\) (since the open circle at \(y = 4\) means \(y = 4\) is not included, and the graph goes up). Wait, but looking at the graph, when \(x = 3\), the open circle is at \(y = 4\), and the graph is above that. So the range is all real numbers greater than 4, or in interval notation \((4,\infty)\)? Wait, no, maybe the open circle is at \((3,4)\), but the graph is actually starting at \(x>3\) and \(y>4\)? Wait, no, let's check the coordinates. The grid: each square is 1 unit. So the open circle is at \(x = 3\), \(y = 4\). The graph then goes through, for example, when \(x = 4\), \(y = 8\)? Wait, no, the y - axis: 2,4,6,8,10,12. So at \(x = 3\), \(y = 4\) (open circle), at \(x = 4\), \(y = 8\)? No, wait, the graph at \(x = 5\) is at \(y = 10\)? Wait, maybe my initial analysis is wrong. Let's re - examine.

Domain: The domain is the set of x - values. The graph starts at an open circle at \(x = 3\) and extends to the right (towards \(x=\infty\)). So the domain is all real numbers \(x\) such that \(x>3\), or in interval notation \((3,\infty)\).

Range: The range is the set of y - values. The graph starts at an open circle at \(y = 4\) (at \(x = 3\)) and extends upwards (towards \(y=\infty\)). Since the point \((3,4)\) is not included (open circle), the range is all real numbers \(y\) such that \(y>4\), or in interval notation \((4,\infty)\).

Answer:

Domain: \((3,\infty)\)
Range: \((4,\infty)\)