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 equation for each type of transformation that can be used to transform f(x) to g(x).

Thank you!!!

A.

See Explanation

B.

Vertical shift:

Horizontal shift:

C.

The horizontal shift is:

The vertical shift is:

Step-by-step explanation:

See attachment for graph

A. The possible transformation from f(x) to g(x)

From the attachment, g(x) can be translated or shifted to f(x) in two possible ways.

1. Horizontal Shift which shifts g(x) by k units to the right

And

2. Vertical Shift which shifts g(x) downwards by k units

B. Solve for k

First, we calculate the equations of both lines.

However, we need to calculate the slope (m) of both to do so:

For f(x)

So:

The equation is then:

Where:

So:

For g(x)

So:

The equation is then:

Where:

So:

So, we have:

For the horizontal shift:

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If then

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So, we have:

Subtract 2x from both sides

Add 10 to both sides

Divide through by 2

For the horizontal shift:

Subtract 2x from both sides

Subtract 6 from both sides

Multiply both sides by -1

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step-by-step explanation: