Question

THIS IS VERY HARD PLSSS

Answer 1

Answer:

$y=3\sqrt{x-1}-7$

Step-by-step explanation:

We are given the function $y=\sqrt{x}$. Let's apply each transformation separately and see what we get. First, let's apply the vertical shift. We are told that the graph shifts downwards by 7 units. In other words, when x is 0, y should be -7 instead of 0. We can accomplish that by changing the y-intercept of the graph and subtracting our function by 7: $y=\sqrt{x} -7$. Notice that the -7 is outside the square root.

Next, we can apply the horizontal transformation. We are told that the graph shifts to the right 1 unit. This means that, for $y=\sqrt{x}$, if y is 0, x should be 1. We can accomplish this by doing $y=\sqrt{x-1}$ (if x = 1, y will be 0). Now, we can combine the two transformations we have done so far: $y=\sqrt{x-1}-7$.

Lastly, we need to vertically stretch the function by a factor of 3. All we have to do here is multiply sqrt(x) by 3 (this way, if x is equal to 1, y should be 3 instead of 1 (3 times x)). So, we get something like this: $y=3\sqrt{x}$. Now, we can combine all of the transformations we did to get our final answer:

$y=3\sqrt{x-1}-7$