Question

The graph shows the function f(x).

On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).

Which equation represents f(x)?
f(x) = Negative RootIndex 3 StartRoot x EndRoot
f(x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot

Answer 1

The equation that represents the given data is  $\RM \\f(x) = -\sqrt[3]{-x} ,$ Option D is the correct answer.

What is a Function ?

It is a statement where two variables , one dependent and one independent are related.

It is given that

a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).

The equation given in the options are

$\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}$

The function goes through (8,2)

Substituting the values

f(x) = -2

f(x) = $\sqrt[3]{7}$

f(x) = -3

f(x) = 2

The equation that represents the given data is

$\RM \\f(x) = -\sqrt[3]{-x} ,$ Option D is the correct answer.

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