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Answer:

So a translation and a rotation and that is it.

D.

Step-by-step explanation:

There is no reflection.

If we had a negative in front of the x there would have been a reflection.

We can definitely tell the graph was translated 3 units up because of the +3.

There are other ways to look at a translation of a line but it has been translated for sure.

It has also been rotated because of the factor of 1/9 in front of x.

Let me show you a graph.

Comparing to y=mx+b where m is slope and b is y-intercept, we see the slope of f(x)=x is 1 and the y-intercept of f(x)=x is 0 while

the slope of g(x)=(1/9)x+3 is (1/9) and y-intercept of g(x)=(1/9)x+3 is 3.

I drew them here on the graph.

I also drew y=x+3 which has slope 1 and y-intercept 3.

So I just wanted to show you have we translate y=x up to y=x+3, you still don't have the same line.  But notice if you rotate y=x+3 using the (0,3) as the center of rotation you could get the green line to lay on the orange line.

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DeanR

Is this supposed to be multiple choice? If so it's a terrible question as the answer is all of the above. I'll sketch out the transformations, avoiding details.

Transform y=x to y=x/9 + 3

a. using rotation and reflection

Rotate around the origin to get y=-x/9 and reflect in y=3/2 to get y=x/9 +3

b. using translation, reflection, rotation

Translate to y = x - 3, reflect in the x axis to get y = x + 3 and rotate around (0,3) to get the result.

c. using translation and reflection.

Translate to y = x + 3 and reflect along the line which bisects the angle at (0,3).

d. rotation and translation

Rotate to a slope of 1/9 and translate up 3 units.

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