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 $4 - \frac{f(x)}{8}$.

Step-by-step explanation:

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

Step 1:

Vertical compression by a factor $\frac{1}{8}$ , this means decreasing value of function by a factor of  $\frac{1}{8}$. Function becomes $\frac{f(x)}{8}$.

Step 2:

Reflection over x-axis means rotating f(x) by 180° over origin . Function now is $-\frac{f(x)}{8}$.

Step 3:

Up 6 , means value of function is increased by 6 , Function now is $\frac{-f(x)}{8} + 6$.

Step 4:

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

∴Function finally becomes, $\frac{-f(x)}{8} +6 - 2$ which is $4 - \frac{f(x)}{8}$.