Question

Explain how the domain of $y=g\left(x\right)=\sqrt{x}$ compares to$y=g(x-k),k\ge 0$

Short answer

The domain of $y=g(x)=\sqrt{x}$ ranges from 0 to $\infty$

where as the domain of $y=g(x-k) ; k \geq 0$ ranges from $k$ to $\infty$

Step-by-step solution

Given information

Given the equation $y=\sqrt{x}$

$y=g(x-k)$

Checking the effect of k

The domain of $y=g(x)=\sqrt{x}$ ranges from 0 to $\infty$

where as the domain of $y=g(x-k) ; k \geq 0$ ranges from $k$ to $\infty$