graphing transformations

[flyingfreedom]

The graph of y = f (x) is shown below on the left. Determine an equation of the function
graphed on the right.
[attachment=0:3gpqke3v]ScreenHunter_03 Jan. 18 15.17.gif[/attachment:3gpqke3v]
I answered C but apparently the correct answer is B. I just cannot understand how the answer could be B.

When you reflect the graph in the x-axis and then compress it vertically by a factor of 1/2 in relation to the vertex, and then move it three up you get the graph on the right.

having expressed that, the answer key is probably right because this is a sample provincial exam.
Is my method right?

 

[soroban]

Hello, flyingfreedom!

Careful . . . We must apply the transformation in the correct order.
I had to baby-talk my way through it . . .

The graph of \(\displaystyle y = f (x)\) is shown below on the left.
Determine an equation of the function graphed on the right.

This is the way I approached this problem . . .

First, I move the function down 4 units.

\(\displaystyle \text{And }\,y \:=\:f(x) - 4 \,\text{ looked like this:}\)

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Then I reduced the vertical displacement by one=half.

\(\displaystyle \text{And }\,y \:=\:\tfrac{1}{2}\left[f(x) - 4\right]\quad\Rightarrow\quad y \:=\:\tfrac{1}{2}f(x) - 2\,\text{ looked like this:}\)

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Finally, I "flipped" the graph over the x-axis.

\(\displaystyle \text{And }\,y \:=\:-\bigg[\tfrac{1}{2}f(x) - 2\bigg]\,\text{ looked this this:}\)

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\(\displaystyle \text{And that's why the answer is: }(B)\;y \:=\:-\tfrac{1}{2}f(x) + 2\)

 

[Artimid]

By the way, I just wanted to say thank you for that well explained answer, Soroban. I was actually recently introduced.. or re-introduced if I forgot, to this process. Your explanation helped push home what the book completely lacked and just assumed we knew. ^_^ Thank you again.