Question

In Desmos, type in both equations:

1. y= square root of x
2. y= square root x-3+4

What transformations occurred in the graph?

Answer 1

$$y=5\sqrt[3]{x+1}$$

Parent function $f(x)=\sqrt[3]{x}.$

To graph $g(x)=\sqrt[3]{x+1},$ we shift the graph of $f$ to the left 1 unit.

To graph $h(x)=5\sqrt[3]{x+1},$ stretch the graph of $g$ vertically by a factor of $5.$Function is given as:

$y=\sqrt[2]{x^{-2}+4}$

$y=\sqrt[2]{\frac{1}{x^2}+4}$

for real solutions of y the term inside the square root should be as:

$\frac{1}{x^2}+4\ge0$

We can se that x has degree two so for all values of x the above term gives always positive values except x=0, as this makes it infinite value i.e. undefined, so the domain of the given equation is as:

Domain = ($-\infty,+\infty$ )-[0] i.e the transformation will lie on x axis