Question

The graphs of functions f(x) and g(x) = f(x) + k are shown below: graph of line f of x going through ordered pairs 0, negative 2 and 2, 2. Graph of line g of x going through ordered pairs 0, 2 and 1, 4. The value of k is ___

Answer 1

The value of k is 4

Step-by-step explanation:

Let us revise the vertical translation

1. If the function f(x) translated vertically up  by k units, then the new

  function g(x) = f(x) + k , that means we add every y-coordinate of the

  points lie on the graph of f(x) by k

Ex: If point (x , y) lies on f(x), then its image is (x , y + k) lies on g(x)

2. If the function f(x) translated vertically down  by k units, then the new

   function g(x) = f(x) – k , that means we subtract every y-coordinate

   of the points lie on the graph of f(x) by k

Ex: If point (x , y) lies on f(x), then its image is (x , y - k) lies on g(x)

∵ g(x) = f(x) + k

∴ g(x) is the image of f(x) by translation k units up

∵ The graph of line f(x) going through ordered pair (0 , -2)

∵ The graph of line g(x) going through ordered pair (0 , 2)

∵ The image of ordered pair(x , y) by translation k units up is

   (x , y + k)

∴ y = -2 and y + k = 2

- Substitute the value of y

∴ -2 + k = 2

- Add 2 to both sides

∴ k = 4

The value of k is 4

V.I.Note:

Point (1 , 4) is not the image of point (2 , 2) because the x-coordinates

of the two points are not equal, vertical translation changes the

y-coordinates only, the image of point (2 , 2) is (2 , 6) and point (1 , 4)

is the image of point (1 , 0)

Learn more:

You can learn more about transformation in brainly.com/question/9381523

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