The graph of y = StartRoot x EndRoot is transformed as shown in the graph below. Which equation represents the transformed function?
On a coordinate plane, a curve opens up and to the right. It starts at (0, 2) and then decreases through (4, 0) into quadrant 4.
y = negative StartRoot x EndRoot
y = StartRoot (negative x) EndRoot + 2
y = StartRoot (negative x) EndRoot minus 2
y = negative StartRoot x EndRoot minus 2
Well, well, well, we seem to have a little transformation on our hands! Let's break it down, shall we? We see that the graph is opening up and to the right, which means it's flipped vertically and shifted upwards. Now, let's take a look at the starting point. It's at (0,2), and since it's flipped vertically, we can say it's at (0,-2) instead. So, after a little bit of clown magic, the equation representing the transformed function would be y = StartRoot (negative x) EndRoot minus 2. Ta-da!
The graph of y = StartRoot x EndRoot is transformed to open up and to the right in the given graph. Moreover, the graph starts at (0, 2) and decreases through (4, 0) into quadrant 4.
To determine the equation that represents the transformed function, we need to consider the following transformations:
1. The negative sign in front of the square root function indicates a reflection across the x-axis.
2. The function passes through (0, 2), indicating a vertical shift upward by 2 units.
3. The function decreases through (4, 0), indicating a horizontal shift to the right by 4 units.
Considering these transformations, the equation that represents the transformed function is:
y = negative StartRoot (x minus 4) EndRoot + 2
Therefore, the correct equation is y = negative StartRoot (x minus 4) EndRoot + 2.
To determine the equation that represents the transformed function, we need to analyze the given information about the graph.
1. The curve opens up and to the right, indicating a reflection about the x-axis and a horizontal shift to the right. These transformations can be achieved by negating the entire function and introducing a horizontal shift.
2. The function starts at (0, 2), which means the y-intercept is 2. This information helps us determine the vertical shift, if any.
3. The graph decreases through (4, 0) into quadrant 4. This implies a compression or vertical stretching of the graph.
Now, let's analyze each given equation to identify the one that satisfies all the conditions:
1. y = negative StartRoot x EndRoot
This equation reflects the graph about the x-axis but does not account for the horizontal shift and vertical shift specified. Therefore, it is not the correct equation.
2. y = StartRoot (negative x) EndRoot + 2
This equation reflects the graph about the y-axis but does not include the horizontal shift to the right. Additionally, it introduces a vertical shift upwards by 2, which is not consistent with the given information. Hence, this is not the correct equation.
3. y = StartRoot (negative x) EndRoot minus 2
This equation reflects the graph about the y-axis and introduces the horizontal shift to the right. However, it also includes a vertical shift downwards by 2, which conflicts with the y-intercept given in the graph. Therefore, this equation is not correct.
4. y = negative StartRoot x EndRoot minus 2
This equation satisfies all the conditions mentioned. It reflects the graph about the x-axis, introduces the horizontal shift to the right, and has the correct y-intercept of 2 (after negation) as given in the graph.
Hence, the correct equation representing the transformed function is:
y = negative StartRoot x EndRoot minus 2.
words, words, words !!
y = √x
you know that it is something like y = -√x
since its vertex is at (0,2) then it looks like
y = -√x + 2
check: -√4+2 = 0 ✅ so it goes through (4,0)
Looks like you have a typo somewhere