1. Drag each tile to the correct location on the inequality. Tiles can be used more than once. Regarding the graphed function, what are its domain and range? These are two separate questions; can someone assist? 2. Which of these graphs represents a function? A) W B) X C) Y D) Z

Mathematics · Middle School · Thu Feb 04 2021

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1. To address the first question about the inequality, it seems like there might have been an intention to include some interactive elements such as tiles, but as this is a text-based medium, I can't provide direct interaction with tiles. Instead, I'll explain how to determine the correct location for tiles in an inequality:

- Start by looking at the inequality symbols given (for example, <, ≤, >, ≥). - Determine the boundaries by observing the constants or expressions the variable is being compared to. - Drag the tiles to their correct positions according to the inequality's direction (for example, if x < 5, the tile with '5' would be on the right side of the 'x' tile, with the less than '<' symbol in between).

For the second part about the domain and range of the graphed function, again, as I can't see the graph, I will explain it in general terms:

Domain: The domain of a function is the set of all possible input values (usually x-values) that the function can accept without resulting in any undefined or non-real numbers. For example, if the graph shows a line or a parabola that continues indefinitely in both left and right directions, the domain is all real numbers, often denoted as (-∞, ∞).

Range: The range of a function is the set of all possible output values (usually y-values) that the function can produce. The range is determined by looking at the vertical extent of the graph. If the graph extends indefinitely upwards and downwards, then the range can also be all real numbers. If the graph has a maximum and/or minimum y-value, then the range is restricted to those values.

2. In general, for a graph to represent a function, it must pass the vertical line test; that is, any vertical line drawn through the graph must intersect the graph at no more than one point. This test ensures that for every input (x-value), there is only one output (y-value), which is a core definition of a function.

Without the images of the graphs labeled as W, X, Y, and Z, I cannot definitively tell you which represents a function. You can use the vertical line test yourself on each graph to determine which one(s) represent functions by simply imagining drawing vertical lines across the graph and seeing if they only touch the graph in one place.