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Michaelyork1495
27.10.2020 •
Mathematics
(Asked 10 TIMES NOW... please help :) Can anyone help me out with this? would be greatly appreciated! on a time crunch. (all questions require a written response, there is no multiple choice.)
Functions and Transformations:
Transformations can be thought of as functions that take the points from one object (the pre-image) to the corresponding points on another object (the image). In the unit, you saw examples of how algebra can be used to rewrite the coordinates of points after they have been transformed. You can also use function notation to rewrite the coordinates. For example, these statements show several different ways you can use function notation for the translation, T, of a point 6 units in the positive x-direction:
T(x, y) = (x + 6, y)
T:(x, y) = (x + 6, y)
T (x, y) = (x + 6, y)
T6, 0(x, y) = (x + 6, y)
Part A: Write functions for each of the following transformations using function notation. Choose a different letter to represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise direction.
translation of a units to the right and b units up
reflection across the y-axis
reflection across the x-axis
rotation of 90 degrees counterclockwise about the origin, point O
rotation of 180 degrees counterclockwise about the origin, point O
rotation of 270 degrees counterclockwise about the origin, point O
Part B: How do these functions differ from functions you have used in algebra in the past?
Part C: In the same way that other functions can be combined, a series of transformations can be combined into a single function. For example, this statement for the function S shows one way to represent the rotation of a point 270° counterclockwise about the origin followed by a translation 3 units to the left and 1 unit up: S(270, O)/ (x, y) = (y – 3, -x + 1).
Write a function to represent each series of transformations:
rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis
reflection across the y-axis, then a translation a units to the right and b units up
translation a units to the right and b units up, then a rotation of 180 degrees counterclockwise about the origin, then a reflection across the y-axis
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Ответ:
The answers are
* For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line.
* If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices.
Step-by-step explanation: Given that the Hernandez family has ordered 3 large pizzas, which they cut so that each pizza has the same number of slices, giving them a total of 24 slices.
So, if 'x' represents the number of pizzas ordered and 'y' represents the number of slices cut from the pizzas, then we have
So, y = 8x represents the relationship between the number of slices and number of pizzas. Here, 8 is the constant of proportionality, which is determined easily.
Also, for the Wilson's family, the equation y = 10x represents the relationship, where x represents the number of pizzas and y represents the number of total slices.
So, both the graph for the relationship for both the families is a straight line and will pass through the origin (0,0), when plot on the coordinate plane. See the attached figure.
Also, if the Wilson family ordered 3 large pizzas, then number of slices
= 10 × 3 = 30>24.
So, number of slices will be more than that of the Hernandez family.
Thus, the correct statements are
* For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line.
* If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices.