Dexter has 56 tiles left over from tiling his bathroom floor and he would like to use them to tile the front entrance of his house. Each tile has an area of 36 in. 2 . The function A(t) 36t represents the area A(t), in
square inches, that t tiles cover. What domain and range are reasonable for the function? What is the graph of the function?
The domain of the function A(t) is the set of possible values for the number of tiles t. In this case, the number of tiles cannot be negative, so the domain is t ≥ 0.
The range of the function A(t) is the set of possible values for the area covered by the tiles. Since each tile has an area of 36 in.2, the area covered will always be a multiple of 36 in.2. Therefore, the range is A(t) = 36t, where t is any non-negative integer.
To graph the function, we can plot points on a coordinate plane. Since each tile has an area of 36 in.2, we can calculate the area covered for different values of t. For example, when t = 0, no tiles are used and the area covered is 0. When t = 1, one tile is used and the area covered is 36 in.2. When t = 2, two tiles are used and the area covered is 72 in.2. We can continue this pattern to find other points.
Using these points, we can plot them on a coordinate plane with t on the x-axis and A(t) on the y-axis. The graph will be a straight line passing through the origin (0,0) and with a slope of 36/1, since each additional tile adds 36 in.2 to the area covered.
The graph will start at the origin and continue indefinitely upward, since there is no limit to the number of tiles that can be used. The points on the graph will form a straight line that gets steeper as t increases.
The domain of the function A(t) is the set of all possible inputs, in this case, the number of tiles (t). Since Dexter has 56 tiles left over from tiling his bathroom floor, the reasonable domain for this function would be the set of whole numbers from 0 to 56, inclusive.
The range of the function A(t) is the set of all possible outputs, in this case, the area (A) covered by the given number of tiles. Since each tile has an area of 36 in², the reasonable range for this function would be the set of all positive multiples of 36.
To graph the function A(t), we can plot the values of t on the x-axis and the corresponding values of A on the y-axis. Since the function is linear, the graph will be a straight line with a positive slope.
Note: Unfortunately, as a text-based AI bot, I am unable to generate or display graphical images.