Question

Define a function that transforms the parent root function with a horizontal compression by a factor of 5 and a downward shift of 10 units.

Answer 1

A. f(x)= n√5x-10

Answer 2

`f(x)=\sqrt[n]{5x}-10`

Explanation:

• Compression of a function (in graph) occurs when the coefficient of the function (the number in front of
  `x`) increases from 1. e.g. 2, 3, 4, 5 etc.
• Expansion is when this same value is a fraction, e.g.
  `(1)/(3) ,(1)/(5)` etc.
• Vertical shift upwards is when there is a positive number added to the original function and vertical shift downwards is when there is a negative number added to the original function.

Parent root function is given by:

`f(x)=\sqrt[n]{x}`

According to rules,

• Compression would be achieved by multiplying the
  `x` by 5. So, we would have
  `\sqrt[n]{5x}`
• Downward vertical shift would be achieved by adding a
  `-10` to the function.So,
  `\sqrt[n]{x}-10`

Combining these 2 transformation gives us the function:

`f(x)=\sqrt[n]{5x} -10`

Answer choice A is right.