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

X=92.49 m

Explanation:

Given that

u= 21 m/s

h= 97 m

Time taken to cover vertical distance h

h= 1/2 g t²

By putting the values

97 = 1/2 x 10 x  t²          ( g = 10 m/s²)

t= 4.4 s

The horizontal distance

X= u .t

X= 21 x 4.4

X=92.49 m