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

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

answer: what is the conflict?

step-by-step explanation:

*what has happened to new york city?

*what is in the time capsule?

* what did the kidz see that gave them hope?

*what will they do with what they find?

* how will they save the city?

* what challenges will they face along the way?

*what big choice will they make at the climax of the story?

* what lesson do they learn at the end of the story?