Answer :
Answer: The equation is y = 0.25/(x - 4) + 3
Step-by-step explanation:
If we have a function y = f(x)
A compression means that we multiply the function by a factor smaller than 1.
Then the vertical compression by a factor of 0.25 is:
y = 0.25*f(x)
a translation by A units to the right, means that we need to valuate the function in x - A.
So now we have:
y = 0.25*f(x - 4)
A translation in the y-axis means that we need to add a constant to the equation, then if we tralate it by 3 units up, we have:
y = 0.25*f(x - A) + 3
Then, if f(x) = 1/x
Our new equation is:
y = 0.25/(x - 4) + 3
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.
[tex]f ( x ) --- > g ( x ) = [ \frac{a}{( x +/- b)} ] + c[/tex]
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