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)

see below

Parts a,b,c are done for each transformation

Step-by-step explanation:

We can shift f(x) to g(x) by  shifting f(x) to the left

y = f(x + k) k > 0 moves it left

f(x) has a point at ( 2,8) and g(x) has a point at (0,8)

0 -2 = -2

We want to move it 2 units to the left so they become the same point

g(x) = f(x+2)

We can shift f(x) to g(x) by  shifting f(x) up

y = f(x) + k  

k > 0 moves it up

f(x) has a point at (0,-2) and g(x) has a point at (0,8)

8 - -2 = 8+2 = 10

We want to move it 10 units up

g(x) = f(x) + 10

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed