MATH SOLVE

3 months ago

Q:
# 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 ___

Accepted Solution

A:

The value of k is 4Step-by-step explanation:Let us revise the vertical translation1. 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 kEx: 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 kEx: 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 = 4The value of k is 4V.I.Note:Point (1 , 4) is not the image of point (2 , 2) because the x-coordinatesof the two points are not equal, vertical translation changes they-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#LearnwithBrainly