Question

Write the function notation for the transformation that would change f(x) to have a vertical

compression by a factor of 1/8, reflection over the x axis, up 6 and right 2

Answer 1

Function is
`4 - (f(x))/(8)`.

Explanation:

We have a function notation for the transformation that would change f(x) to have a vertical compression by a factor of
`(1)/(8)`, reflection over the x axis, up 6 and right 2.

Step 1:

Vertical compression by a factor
`(1)/(8)` , this means decreasing value of function by a factor of
`(1)/(8)`. Function becomes
`(f(x))/(8)`.

Step 2:

Reflection over x-axis means rotating f(x) by 180° over origin . Function now is
`-(f(x))/(8)`.

Step 3:

Up 6 , means value of function is increased by 6 , Function now is
`(-f(x))/(8) + 6`.

Step 4:

Right 2, means shifting function to 2 units on right side i,e, on x-axis.

∴Function finally becomes,
`(-f(x))/(8) +6 - 2` which is
`4 - (f(x))/(8)`.