Question

A function $f$is given, and the indicated transformations are applied to its graph (in the given order). Write an equation for the final transformed graph.

$f\left(x\right)=\sqrt[3]{x}$; shift$1$ unit to the right

Short answer

The transformed equation is$f\left(x\right)=\sqrt[3]{x-1}$

Step-by-step solution

Step 1. Concept of transformation in left or right direction.

To graph $y=f(x-c)$, shifts the graph$y=f\left(x\right)$ to the right$c$units

And, to graph$y=f(x+c)$ shifts the graph$y=f\left(x\right)$ to the left $c$units

Step 2. Given Problem.

Given that,

$f\left(x\right)=\sqrt[3]{x}$; shifts $1$units to the right

Step 3. Determining the transformed equation.

Here,$1$ is a constant which is shifted right

So, the transformed equation is

$f\left(x\right)=\sqrt[3]{x-1}$