Question

The graph models the projected populations, in thousands, of two towns after x years. both towns experience a 1.9% annual growth rate. which equation represents g(x) as a transformation of f(x)?

a. g(x) = f (x+3/5)
b. g(x) = f (x-5/3)
c. g(x) = f (x) + 3/5
d. g(x) = 5/3 * f(x)

Answer 1

D.)

Explanation:

Answer 2

d. g(x) = 5/3 * f(x)

Explanation:

A transformation is the movement of a point from its initial position to a new position. Transforming an object involves transforming all the points in the object. Types of transformation are rotation, reflection, dilation and translation.

From the graph When x = 0, y = f(0) = 30, also when x = 16, y = f(16) = 40

For the graph of g(x), when x = 0, y = g(0) = 50 and when x = 16, y = g(16) = 67

This means that g(x) = 5/3 * f(x), g(0) = 5/3 * f(0) = 5/3 * 30 = 50, also g(16) = 5/3 * f(16) = 5/3 * 40 = 67