Answer:
[tex]f(x)=\sqrt[n]{5x}-10[/tex]
Step-by-step explanation:
- Compression of a function (in graph) occurs when the coefficient of the function (the number in front of [tex]x[/tex]) increases from 1. e.g. 2, 3, 4, 5 etc.
- Expansion is when this same value is a fraction, e.g. [tex]\frac{1}{3} ,\frac{1}{5}[/tex] 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:
[tex]f(x)=\sqrt[n]{x}[/tex]
According to rules,
- Compression would be achieved by multiplying the [tex]x[/tex] by 5. So, we would have [tex]\sqrt[n]{5x}[/tex]
- Downward vertical shift would be achieved by adding a [tex]-10[/tex] to the function.So, [tex]\sqrt[n]{x}-10[/tex]
Combining these 2 transformation gives us the function:
[tex]f(x)=\sqrt[n]{5x} -10[/tex]
Answer choice A is right.
