Question

The function f(x) = x3 is translated such that the function describing the translated graph is g(x) = (x + 5)3 + 2.Where is the point (0, 0) for the function f now located on the function g?

Answer 1

Answer:

(-5,2)

Step-by-step explanation:

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Answer 2

The point (0,0) for the function f is now located at (-5,2) on the function g.

What is transformation of the function?

The transformation of the function is defined as the shifting of the function to a new position.

If a function f(x) is shifted a to left then the function will be f(x+a) and a to right then the function will f(x-a).

If a function f(x) is shifted a to up then the function will be f(x)+a and a to down then the function will f(x)-a.

So here the original function is f(x)=x³

After transformation function is g(x)= (x+5)³+2

which we can write as g(x)=f(x+5)+2

from the expression of the function g(x) it is clear that first f(x) is translated to left by 5 for which the function becomes f(x+5) then the function is translated to up by position 2 then the function becomes f(x+5)+2.

So, The function g(x) is obtained by shifting the graph of the parent function f(x) by 5 units left and then 2 units up.

Therefore transformation is the form

g(x)=f(x+5)+2

so, the transformed function has equation:

g(x)= (x+5)³+2

Like the function, the point (0, 0) for the function f is also shifted by 5 units left and then 2 units up.

Then the point (0, 0) for the function f is located at (-5,2).

Therefore The point (0,0) for the function f is now located at (-5,2) on the function g.

Learn more about transformation of the function

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