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The graph of y=x^3 is transformed as shown in the graph below. With. Equation represents the transformed function

The graph of y=x^3 is transformed as shown in the graph below. With. Equation represents-example-1
User Nyc
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1 Answer

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Answer: y' = (-x)^3 - 4

Explanation:

The graph y = f(x) = x^3 passes trough the point (0,0)

because when x = 0

f(0) = y = 0^3 = 0

in the graph of the image, we can see that the graph intersects the y-axis in the point (0, -4)

This means that we have a vertical displacement of 4 units downwards.

When we have a graph y = f(x), a vertical translation of A units can be written as

y' = f(x) + A

If A is positive, the displacement is upwards, if A is negative, the displacement is downwards.

So if the displacement is of 4 units down, A = -4

We also have that when x is negative, the value of y is positive.

But in our original function, we have that for x = -1, y = (-1)^3 = -1

so in our original function, when x is negative also does y.

Then we also did a reflection around the y-axis, this means that we now evaluate the function in -x instead of x.

So the equation of the graph is:

y' = (-x)^3 - 4

User Yury Bayda
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