Answer:
g ( x ) = 0.25 / ( x - 4 ) + 3
Step-by-step explanation:
Solution:-
- The given function is defined as an inverse function:
f ( x ) = 1 / x
- The transformation on the function of f ( x ) are of three kinds. We will use a general form to look at the effect of each transformation.
![f ( x ) --- > g ( x ) = [ \frac{a}{( x +/- b)} ] + c](https://tex.z-dn.net/?f=f%20%28%20x%20%29%20---%20%3E%20g%20%28%20x%20%29%20%3D%20%5B%20%5Cfrac%7Ba%7D%7B%28%20x%20%2B%2F-%20b%29%7D%20%20%5D%20%2B%20c)
Where a,b, and c are constants for transformation.
- The effect of constant a:
a > 1 ------ > Flattens the graph
0 < a < 1 -------- > Compresses the graph vertically
- The effect of constant b:
b > 0 ------ > Horizontal shift to left
b < 0 -------- > Horizontal shift to right
- The effect of constant c:
c > 0 ------ > Vertical shift up
c < 0 -------- > Vertical shift down
- Now we will determine the result of function after each transformation.
- Compressed vertically by a factor of 0.25. Hence, a = 0.25 [ 0 , 1 ]
k ( x ) = 0.25 / x
- Translated 4 units right. The value of b = -4 , right shift : b < 0.
j ( x ) = 0.25 / ( x - 4 )
- translated 3 units up. The value of c = 3, up shift. c > 0
g ( x ) = 0.25 / ( x - 4 ) + 3
Hence, the resulting function of all the mentioned transformations of original function f ( x ) is given as g ( x ):
g ( x ) = 0.25 / ( x - 4 ) + 3