Question

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the domain and range of part of a linear function g are given below.
$x > 4$ and $y < 5$
which graph could represent this part of linear function g?

Explanation:

Step1: Analyze Domain Condition

The domain is \( x > 4 \), so the graph should have points where the x - coordinate is greater than 4. This means the line segment or ray should start (or be defined) for x - values to the right of \( x = 4 \) (open circle at \( x = 4 \) if it's a ray or segment starting there).

Step2: Analyze Range Condition

The range is \( y < 5 \), so the y - coordinates of the points on the graph should be less than 5. This means the line should be below \( y = 5 \), and if there is a boundary at \( y = 5 \), it should be an open circle (since \( y
eq5 \)). Also, for a linear function, the slope will determine the direction, but the key is the position relative to \( x = 4 \) (domain) and \( y = 5 \) (range). We need to check the graphs (not shown here, but in general) for a linear graph where \( x>4 \) (so the graph is to the right of \( x = 4 \)) and \( y < 5 \) (graph is below \( y = 5 \)). A linear function with domain \( x>4 \) and range \( y < 5 \) should be a ray (or part of a line) that starts at \( x>4 \), has \( y \) - values less than 5, and has a slope that is consistent (since it's linear). For example, if the linear function has a negative slope, as \( x \) increases (since \( x>4 \)) from 4, \( y \) would decrease towards values less than 5, or with a positive slope, but still \( y<5 \) for \( x > 4 \). But the main visual checks are the x - domain (right of \( x = 4 \)) and y - range (below \( y = 5 \)).

Answer:

(The graph that has \( x>4 \) (e.g., open circle or no point at \( x\leq4 \)) and \( y < 5 \) (open circle or all points below \( y = 5 \)) for the linear function. Since the graphs are not shown, in a typical problem, the correct graph would be the one with a ray starting at \( x>4 \) (open circle at \( x = 4 \)) and \( y \) - values less than 5 (open circle at \( y = 5 \) if it's a boundary) and a linear trend consistent with the domain and range. For example, if there are options, the one with \( x>4 \) (right of \( x = 4 \)) and \( y < 5 \) (below \( y = 5 \)) for the linear part.)