Suppose (3,2) is a point on the graph of y=g(x) What point is on the graph of y=-3g(x-7)+1?

Question

What point is on the graph of y=-3g(x-7)+1?

Answer 1

Translating y = g(x) 7 units to the right yields y = g(x-7). So, the point (3,2) moves to (10, 2).

Vertically stretch by a factor of 3 and reflect in the x-axis to get y = -3g(x-7). So, (10, 2) moves to (10, -6).

Finally, translate vertically up 1 unit to get y = -3g(x-7) + 1. So, (10, -6) moves to (10, -5)

ANSWER: (10, -5)

Answer 2

y = g(x); g(3) = 2

Assumption:

y = g(x)

and

y = - 3 * g(x - 7) + 1

therefore,

g(x) = - 3 * g(x - 7) + 1

If x = 3, then

g(3) = 2 = - 3 * g(3 - 7) + 1

2 = - 3 * g(- 4) + 1

1 = - 3 * g(- 4)

-1/3 = g(- 4)

Ans: (- 4, - 1/3)

If the assumption above is correct, then the answer is also correct.

Best,

Gary