Question

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).

Answer 1

Answer:

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).

Step-by-step explanation:

The given function is

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

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  $f(x) \implies f(-x)$, that means we need to multiply the x-variable by -1.

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

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

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.

Answer 2

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:

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

The rule of reflection over the x-axis is:

$(x,y) \to (x-y)$

This means that:

$g(x) = -f(x)$

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

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

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

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