The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear functions; f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Part B: Solve for k in each type of transformation. (4 points)

Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Part A: 1) A horizontal translation f(x + k, y) → g(x, y)

2) A vertical translation f(x, y + k) → g(x, y)

Such that we have, f(0, -2 + k) → g(0 , 8)

Part B:

k = -2 (Horizontal translation)

k = 10 (Vertical translation)

Part C:

The equations are;

g(x) = -2 + f(x)

g(y) = 10 + f(y)

Step-by-step explanation:

The given parameters are;

f(x) pass through (1, 3) and (3, 13)

g(x) pass through (-1, 3) and (1, 13)

Part A: Given that the lines are infinitely long, and that the lines are parallel, the two types of transformation are;

1) A horizontal translation f(x + k, y) → g(x, y)

Such that we have, f(1 + k, 3) → g(-1, 3)

2) A vertical translation f(x, y + k) → g(x, y)

Such that we have, f(0, -2 + k) → g(0 , 8)

Part B:

1) Given that 1 + k= -1, we have;

k = -1 - 1 = 1 + 1 = -2

k = -2

2) 1) Given that -2 + k = 8 , we have;

k = 8 + 2 = 10

k = 10

Part C:

The equations are;

g(x) = -2 + f(x)

g(y) = 10 + f(y)