Let g(x) be the indicated transformation of f(x). write the rule for g(x)
linear function defined by the table, vertical translation 1.5 units up.
x -2 -1 0
f(x) 3.5 2 0.5
include explanation

f(x) = -1.5 x + 0.5

Step-by-step explanation:

* Lets explain how to solve the problem

- The form of the linear function is f(x) = mx + c, where m is the slope

 of the line which represents the function and c is the y-intercept

- The y-intercept is the intersection between the graph of the function

  and the y-axis at point (0 , c)

- The rule of the slope of a line whose endpoints are

  and   is

- If the function f(x) translated vertically up  by k units, then the

 new function g(x) = f(x) + k

- If the function f(x) translated vertically down by k units, then the

 new function g(x) = f(x) – k

∵ f(x) represented by the table:

  x   :    -2    ,    -1    ,    0

  f(x):   3.5    ,    2    ,   0.5

∴ The line which represent the linear function f(x) contains the

   points (-2 , 3.5) , (-1 , 2) , (0 , 0.5)

- Let = (-2 , 3.5) and = (-1 , 2)

∴ The slope of the function  

∴ = -1.5

∵ The function f(x) = mx + c

∵ m = -1.5 and c = 0.5

∴ f(x) = -1.5 x + 0.5

∵ g(x) is the translation of f(x) 1.5 units up

- According to the rule of translation above

∴ g(x) = f(x) + k

∵ k = 1.5

∵ f(x) = -1.5 x + 0.5

∴ g(x) = -1.5 x + 0.5 + 1.5

∴ g(x) = -1.5 x + 2

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation: