Math

QuestionFind the equation for the function shaped like f(x)=x2f(x)=x^{2}, shifted 3 right and 7 down: g(x)=g(x)=

Studdy Solution

STEP 1

Assumptions1. The function f(x)=xf(x)=x^{} is the original function. . The new function g(x)g(x) is a transformation of f(x)f(x).
3. The transformation involves a shift of three units to the right and seven units down.

STEP 2

The general form of a function that has been shifted horizontally and vertically is given byg(x)=f(xh)kg(x) = f(x - h) - kwhere hh is the horizontal shift and kk is the vertical shift.

STEP 3

In this case, the function is shifted3 units to the right and7 units down. Therefore, h=3h =3 and k=7k =7.

STEP 4

Substitute the values of hh and kk into the general form of the function.
g(x)=f(x3)7g(x) = f(x -3) -7

STEP 5

Now, substitute the original function f(x)=x2f(x) = x^{2} into the equation.
g(x)=(x3)27g(x) = (x -3)^{2} -7So the equation for the function whose graph is the shape of f(x)=x2f(x)=x^{2}, but shifted three units to the right and seven units down is g(x)=(x3)27g(x) = (x -3)^{2} -7.

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