The function y=f(x) is transformed to g(x)= 1/2f[-1/3(x+4)]-7. If point c’ (-19,-3) is on the function g(x), then the coordinates of point c on the function f(x) are

(53, -17/2)

Step-by-step explanation:

When you have transformatons a * f(b(x-c)) + d there are two steps to transform.

Step 1, multiply x by 1/b and multiply y by a  pay attention to posities and negatives.

Step 2 add c (keep in mind if you have -c you add c and if you have +c you subtract) to x and d to y.

In your example the transformation is 1/2 f(-1/3 (x+4)) - 7 so

a = 1/2

b = -1/3

c = 4

d = -7

and the point is initially (-19, -3)

Now lets do the two steps

multiply x by 1/b and multiply y by a  pay attention to posities and negatives.

b = -1/3 so 1/3 = -3 and a = 1/2 x = -19 and y = -3  So we do -19 * -3 and -3 * 1/2.  This gives us the new point (57, -3/2)

Now step 2 add c (keep in mind if you have -c you add c and if you have +c you subtract) to x and d to y.

Now our point is (57, -3/2) and c = 4 and d = -7  so we do 57-4 and -3/2 - 7

This gets us (53, -17/2)

Let me know if there is anything you don't understand.

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.