Question

The graph of g(x) is a reflection and translation of f (x) = RootIndex 3 StartRoot x EndRoot.
On a coordinate plane, a cube root function goes through (0, 1), has an inflection point at (1, 0), and goes through (2, negative 1).
Which equation represents g(x)?
g (x) = RootIndex 3 StartRoot x + 1 EndRoot
g (x) = RootIndex 3 StartRoot x minus 1 EndRoot
g (x) = Negative RootIndex 3 StartRoot x + 1 EndRoot
g (x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot

Answer 1

Answer: The equation of the function is $g(x)=-\sqrt[3]{x-1}$.

Given: A function $f(x)=\sqrt[3]{x}$.

To find: Equation for $g(x)$.

Step-by-step explanation:

Step 1: The given graph goes through three point (0, 1), (1, 0) and (2, -1). Thus these point must be satisfy the graph of g(x).

Now, let's check for all the given graph for these three points.

Step 2: For $g(x)=\sqrt[3]{x+1}$.

At x=0 g(x)=1

At x=1 g(x)=$\sqrt{2}$

At x=2 g(x)=$\sqrt[3]{3}$

Here we can see that all points is not satisfying the equation of g(x).

So, it is not representing g(x).

Step 3: For $g(x)=\sqrt[3]{x-1}$.

At x=0 g(x)=$\sqrt[3]{-1}$

At x=1 g(x)=0

At x=2 g(x)=1

Here we can see that all points is not satisfying the equation of g(x).

So, it is not representing g(x).

Step 4: For $g(x)=-\sqrt[3]{x+1}$.

At x=0 g(x)= -1

At x=1 g(x)=$-\sqrt[3]{2}$

At x=2 g(x)= $-\sqrt[3]{3}$

Here we can see that all points is not satisfying the equation of g(x).

So, it is not representing g(x).

Step 5: For $g(x)=-\sqrt[3]{x-1}$.

At x=0 g(x)= 1

At x=1 g(x)=0

At x=2 g(x)= -1

Here we can see that all points is satisfying the equation of g(x).

So, it is representing g(x).

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