Let g(x) be the indicated transformation of function f(x). Write the rule for g(x) linear function defined by the table ,vertical translation by factor 1.5units up. x -2 -1 0 f(x) 3.5 2 0.5
Answers
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
(x_{1},y_{1})(x
1
,y
1
) and (x_{2},y_{2})(x
2
,y
2
) is
m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}m=
x
2
−x
1
y
2
−y
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})(x
1
,y
1
) = (-2 , 3.5) and (x_{2},y_{2})(x
2
,y
2
) = (-1 , 2)
∴ The slope of the function m=\frac{2-3.5}{-1--2}}
∴ m=\frac{-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