Question

График какой функции получится, если: а) параболу у= -1/3х² перенести на 2 единицы вправо и на 3 единицы вверх; б) гиперболу у=3/х перенести на 1 единицу влево и на 2 единицы вниз; в) график функции у= -√х перенести на 4 единицы влево и на 2 единицы вниз; г) график функции у= -|х| перенести на 6 единиц вправо и на 3 единицы вверх?

Answer 1

Ответ:

ответ на картинке держите

Answer 2

Graph Transformations

a) To shift the graph of the parabola y = -1/3x^2 two units to the right and three units up, we can apply the following transformations: - Horizontal shift: x - 2 - Vertical shift: y + 3

b) To shift the graph of the hyperbola y = 3/x one unit to the left and two units down, we can apply the following transformations: - Horizontal shift: x + 1 - Vertical shift: y - 2

c) To shift the graph of the function y = -√x four units to the left and two units down, we can apply the following transformations: - Horizontal shift: x + 4 - Vertical shift: y - 2

d) To shift the graph of the function y = -|x| six units to the right and three units up, we can apply the following transformations: - Horizontal shift: x - 6 - Vertical shift: y + 3

Let's examine each transformation in detail.

Transformation of the Parabola (a)

The original equation is y = -1/3x^2. To shift the graph two units to the right, we replace x with (x - 2). To shift the graph three units up, we replace y with (y + 3).

The transformed equation becomes: y + 3 = -1/3(x - 2)^2

Transformation of the Hyperbola (b)

The original equation is y = 3/x. To shift the graph one unit to the left, we replace x with (x + 1). To shift the graph two units down, we replace y with (y - 2).

The transformed equation becomes: y - 2 = 3/(x + 1)

Transformation of the Function (c)

The original equation is y = -√x. To shift the graph four units to the left, we replace x with (x + 4). To shift the graph two units down, we replace y with (y - 2).

The transformed equation becomes: y - 2 = -√(x + 4)

Transformation of the Function (d)

The original equation is y = -|x|. To shift the graph six units to the right, we replace x with (x - 6). To shift the graph three units up, we replace y with (y + 3).

The transformed equation becomes: y + 3 = -|x - 6|

Please note that these transformations affect the position of the graph but do not change its shape.