Answer:
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
[tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- 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 [tex](x_{1},y_{1})[/tex] = (-2 , 3.5) and [tex](x_{2},y_{2})[/tex] = (-1 , 2)
∴ The slope of the function [tex]m=\frac{2-3.5}{-1--2}}[/tex]
∴ [tex]m=\frac{-1.5}{1}}[/tex] = -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
