Question

Suppose that f(x) is a function and that g(x) is a transformation of f(x) : g(x)=4f(3x−2) If the point (22,9) is on the graph of f(x), find a point which must be on the graph of g(x). Suppose that f(x) is a function and that g(x) is a transformation of f(x) : g(x)=4f(3x−2) If the point (−15,76) is on the graph of g(x), find a point which must be on the graph of f(x).

Answer 1

A point on the graph of g(x) when the point (22,9) is on f(x) is (2.33, 9).

Step-by-step explanation:

To find a point on the graph of g(x), we substitute the given point (22,9) into the equation for g(x). First, we need to find the corresponding value of x for the point (22,9) on the graph of g(x). Rearranging the equation, we have 3x - 2 = (22 - 2)/4 = 20/4 = 5. Solving for x, we get x = (5 + 2)/3 = 7/3 = 2.33. Therefore, a point on the graph of g(x) is (2.33, 9).