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). (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:

Two types of translation are;

1) Horizontal translation left T(0, 8),

2) Vertical translation T(16, 0)

Part B:

For the horizontal translation transformation, k = 8

For the vertical translation transformation, k = 16

Part C:

For the horizontal translation transformation, the equation is f(x + 8) = g(x)

For the vertical translation transformation, the equation is f(x) + 16 = g(x)

Step-by-step explanation:

The equation of the function f(x) is found as follows;

The slope of f(x) = 10/5 = 2

The y-intercept = -10

Therefore, f(x) = y = 2·x - 10

The equation of the function g(x) is found as follows;

The slope of g(x) = 6/3 = 2

The y-intercept = 6

Therefore, g(x) = y = 2·x + 6

Part A:

The transformations are;

Horizontal translation

f(x + k) = g(x)

Vertical translation;

f(x) + k = g(x)

Part B:

For the horizontal translation, we have;

f(x + k) = g(x)

f(x + k) = 2·(x + k) - 10 =2·x + 2·k -10 = g(x)

∴ 2·x + 2·k -10 = 2·x + 6

2·k = 16

k = 8

For vertical translation we have;

Given that f(x) + k = g(x), we have;

2·x - 10  + k = 2·x + 6

k = 6 + 10 = 16

Part C:

For the horizontal translation, we have;

f(x + 8) = g(x)

2·(x + 8) - 10 = 2·x + 6

For vertical translation we have;

Given that f(x) + 16 = g(x), we have;

2·x - 10  + 16 = 2·x + 6

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step-by-step explanation: ; )

a negative exponent is translated as follows:

so, we have