Question

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

Please include explanation

Answer 1

f(x) = -1.5 x + 0.5

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

`(x_(1),y_(1))` and
`(x_(2),y_(2))` is

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

- 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
`(x_(1),y_(1))` = (-2 , 3.5) and
`(x_(2),y_(2))` = (-1 , 2)

∴ The slope of the function
`m=(2-3.5)/(-1--2)}`

∴
`m=(-1.5)/(1)}` = -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