The function f(x) = RootIndex 3 StartRoot x EndRoot is reflected over the x-axis to create the graph of g(x) = Negative RootIndex 3 StartRoot x EndRoot.

Which is the graph of g(x)?

On a coordinate plane, a cube root function goes through (negative 2, negative 8), has an inflection point at (0, 0), and goes through (2, 8).
On a coordinate plane, a cube root function goes through (negative 2, 8), has an inflection point at (0, 0), and goes through (2, negative 8).
On a coordinate plane, a cube root function goes through (negative 8, 2), has an inflection point at (0, 0), and goes through (8, negative 2).
On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).

The function is reflected over the x-axis, this means the values in the range set change to its opposite, all positive elements change to negative, and all negative elements change to positive.

This transformation is defined [tex]f(x) \implies f(-x)[/tex], that means we need to multiply the x-variable by -1.

[tex]g(x)=\sqrt[3]{-x}[/tex]

And it's equivalent to [tex]g(x)=-\sqrt[3]{x}[/tex]

In the image, you can observe that the transformation we applied is an actual reflection over the x-axis. The blue curve represents the transformed function.

Therefore, the right answer is C.

MrRoyal MrRoyal · Answer 2 · 2021-12-15T20:23:22+01:00

Transformation involves changing the form of a function.

The graph of g(x) is (c) Cube root function goes through (-8, 2), has an inflection point at (0, 0), and goes through (8, -2).

The function f(x) is given as:

[tex]f(x) = \sqrt[3]{x}[/tex]

The rule of reflection over the x-axis is:

[tex](x,y) \to (x-y)[/tex]

This means that:

[tex]g(x) = -f(x)[/tex]

Substitute the expression for f(x) in the above equation

[tex]g(x) = -\sqrt[3]{x}[/tex]

Hence, the graph of g(x) is graph (c)

Read more about function transformation at:

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