Question

The graph of y=√x is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph off(x)?$ 10-10-88 10 x

Answer 1

Step-by-step explanation

We must apply some transformations to the function:

`y=g(x)=\sqrt[3]{x}.`

(1) A reflection across the y-axis is given by the transformation:

`g(x)\rightarrow h(x)=g(-x)=\sqrt[3]{-x}=-\sqrt[3]{x}.`

(2) A translation down 2 units is given by the transformation:

`h(x)\rightarrow f(x)=h(x)-2=-\sqrt[3]{x}-2.`

Plotting the function f(x), we get the following graph:

Answer