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Both students are correct because when you substitute 1 for x in each function, the functions will both be equal to 3. Also, when you substitute 0 in for x in the functions, you will end up with 0 each time.

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Both students are correct because when you substitute the x-coordinate of 1 it results in the same y-coordinate

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Both students are correct because if you substitute x for 1 in either equation, the output for both graphs will be 3

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They are both correct since plugging in an x value of 1, they value ends up being 1, for both

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Both students are correct. If you substitute the x-value 1 of one of the points, they both result in the same y-value (3) being produced

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Both students are correct, when x is substituted for 0 the y value is also 0, and (0,0) is the initial point. In either equation when 1 is substituted for x the y value will be 3.

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Both students are correct because if you plug in x values for both functions, the y values are the same.

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Both students are correct because the horizontal compression by 9 and vertical stretch by 3 are the same for the end result

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They both are correct, because when plugging the equation in, both ways work. Either it shows the graph being compressed to that a point from further down on the x-axis shows as a closer point or the graph is vertically stretched such that the point is higher than that of the parent

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both students are right, square root 9x is the same as 3 square root x.

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Both students are correct since the first equation calls for a vertical stretch. The point on the parent function would be (1,1), so the corresponding point on y = 3√x should be (3,1), and this is the case. A point on the parent function would be (3,9). Thus, for the corresponding point on the second function (y = √9x) should be (3,1), and this is the case.

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Both students are correct. The second student's equation can be simplified because 9 is a perfect square. It can be simplified to the first person's equation, which represents the graph because it is a vertical stretch by a factor of three.

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Both - each passes through the initial point at x=1 root(9*1) or 3*root(1) and also does not have any translations to move the initial point.

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They are both the same because if you plug in the x value as 1, then the y values are the same.

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Both students are correct since the first student vertically stretched the graph by 3 and the second student horizontally compressed the graph by a factor of 9, which would result in the same transformed graph

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Both of the students are correct because in this case a horizontal compression is the same as a vertical stretch with these factors.

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Both students are correct, even though their answers are written differently. The first one is a vertical stretch by 3 and the second one is a horizontal compression by 9. They result in the same point, (1,3), when x is plugged in as 1.

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Both students are correct, as the vertical stretch and horizontal compression performed give graphs that pass through those points.

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Both students are correct because if both students plug in the same x values, they will get the same y values

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They are both correct since by substituting an x value of 1 yields 3 for both.

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Both students are correct. When 0 and 1 are plugged into the equation as x, the outcome is the same.

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I think that they are both correct. y=3sqrt(x) and y=sqrt(9x) are the same, because the square of 9 would be 3, and y=3sqrt(x) is correct.

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Both of the responses are correct. If you plug in x as 1 for the first one, you get 3(1) which is three. If you plug in one for the second one, you get the square root of 9(1) which is also three. Since root nine is equal to three, you can factor it out and get 3 times the root of x.

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Both students are correct becuase it is  a vertical stretch by a factor of 3 from the parent function. (1,1) --> (1,3) for the first one and the second sudent does a horizontal stretch by a factor of 9 which is also (1.3)

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The first student is correct because from the parent function, the graph has to be vertically stretched by a factor of 3

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There are both the same because if you plug in x=1 for both equations you will get an output of 3 in both. This can also be tested with another point such as x=4 because in both equations your output will be 6.

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They are both the same, as the compression results in the same graph as the vertical stretch. The way to get to the graph, however, is different for both. The first one multiples the y-value of the point shown by 3, while the second one divides the x-value of a point at y=3 to become the point shown. Thank you for listening to my answer, I'm sorry I got it wrong at first. But thank you.

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Two students' responses to one of the HW questions are shown below.  Who is correct?  Explain.

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Two students' responses to one of the HW questions are shown below.  Who is correct?  Explain.