Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k
3
1/3
-1/3
-3

Option A (3).

Step-by-step explanation:

First step in this question is to identify f(x). Since f(x) is a linear function, therefore, the equation of the straight line is given by the following formula:

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1); where (x, y) is the general point, (x1, y1) is the first point on the line, and (x2, y2) is the second point on the line.

From the graph, it is given that (x1, y1) = (3, 2) and (x2, y2) = (2, 0):

(y - 2)/(x - 3) = (0 - 2)/(2 - 3).

(y - 2)/(x - 3) = (-2)/(-1).

(y - 2)/(x - 3) = 2.

Cross multiplying:

(y - 2) = 2(x - 3).

y - 2 = 2x - 6.

y = 2x - 4.

This the equation of f(x) in the y = mx + c form. To calculate g(x), it is important to note that f(0) = g(k*0) because this simplifies to f(0) = g(0). This means that y-intercept of both the equations is same. The y-intercept of f(x) is -4. Which means that y-intercept of g(x) is -4. This is one point (0, -4). From the graph, another point which passes through g(x) is (1, 2).

it is given that (x1, y1) = (0, -4) and (x2, y2) = (1, 2):

(y - (-4))/(x - 0) = (2 - (-4))/(1 - 0).

(y + 4)/(x) = (6)/(1).

(y + 4)/x = 6

Cross multiplying:

y + 4 = 6x

y = 6x - 4.

In short, f(x) = 2x - 4 and g(x) = 6x - 4

It is given that g(x) = f(k*x). Since f(k*x) = 2*kx - 4, therefore:

6x - 4 = 2*kx - 4.

6x = 2*kx.

2k = 6.

k = 3.

Therefore, Option A is the correct choice!!!