Question

The function f(x) = 3 (Square root of X) is reflected over the x-axis to create the graph of g(x) = .

Which is the graph of g(x)?

Answer 1

Third Graph

Explanation:

We are given the function,
`f(x)=\sqrt[3]{x}`.

The function f(x) is reflected over x-axis to form a new function g(x).

As we know,

'Reflection over x-axis flips the graph of the function and we get, f(x) becomes -f(x)'.

So, reflecting
`f(x)=\sqrt[3]{x}` over x-axis gives the function,
`g(x)=-\sqrt[3]{x}`.

After plotting the function,
`g(x)=-\sqrt[3]{x}`.

We see that, from the options, the third graph matches the graph of
`g(x)=-\sqrt[3]{x}` as below.

Answer 2

The answer is the third graph.

I attach the graph again to avoid misunterstandings.

To find the reflection over the x - axis, just note that f(x) becomes - f(x), so the graph of ∛x is - ∛x.

Graphically is pretty easy because you just have to translate all the points of f(x) to the opposite side across the x-axis.