PLEASE HELP ME PLEASE the linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x). PART A: describe two types of transformations that can be used to transform f(x) to g(x). PART B: solve for k in each type of transformation. PART C: write an explanation for each type of transformation that can be used to transform f(x) to g(x).

Part A;

The two types of transformation are;

1) An horizontal translation of f(x) to the left

2) A vertical translation of f(x) upwards

Part B

For the horizontal translation, k = 8

For the vertical translation, k = 16

Part C:

The explanation for the transformation are as follows

For the horizontal translation, we have, T(8, 0), the number 8 is added to each x-coordinate value, of f(x), to get the coordinates of the corresponding point of g(x)

For the vertical translation, we have, T(0, 16), the number 16 is added to each y-coordinate value, of f(x), to get the coordinates of the corresponding point of g(x)

Step-by-step explanation:

Part B

For the horizontal translation

Let the f(x + k) = g(x)

By inspection, we have;

f(x) = 2·x - 10 and g(x) = 2·x + 6

f(x + k) = g(x) gives;

2 × (x + k) - 10 = 2·x + 6

2·x + 2·k - 10 = 2·x + 6

2·k - 10 = 6

2·k  = 6 + 10 = 16

k = 16/2 = 8

k = 8

For the vertical translation

Let the f(x) + k = g(x)

By inspection, we have;

f(x) = 2·x - 10 and g(x) = 2·x + 6

f(x)+ k  = g(x) gives;

2·x - 10 + k = 2·x + 6

k - 10 = 6

k = 16

Part C:

The explanation for the transformation are as follows

For the horizontal translation, we have, T(8, 0), the number 8 is added to each x-coordinate value, of f(x), to get the coordinates of the corresponding point of g(x)

For the vertical translation, we have, T(0, 16), the number 16 is added to each y-coordinate value, of f(x), to get the coordinates of the corresponding point of g(x).

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: