on a graph there are 3 points,
(-3,0) (0,2) (1,0)
now, by using transformations, y= f(x)+1
is the answer: (-3,1) (0,3) (1,1) ??
and also y= -f(x-2) (using original points)
is it (-3,2) (0,0) (1,2)
or is it (-3,-2) (0,-4) (1,-2) ??
im not sure in what order you have to reflect over the x-axis and then shift right
To apply transformations to a graph, you need to understand the order in which they are applied. Let's examine each question separately:
Question 1: By using the transformation y = f(x) + 1 on the graph with the points (-3,0), (0,2), and (1,0).
To apply the transformation y = f(x) + 1, you need to add 1 to the y-coordinate of each point. Let's go point by point:
For the point (-3,0), adding 1 to the y-coordinate gives (-3,1).
For the point (0,2), adding 1 to the y-coordinate gives (0,3).
For the point (1,0), adding 1 to the y-coordinate gives (1,1).
Therefore, the transformed points would be (-3,1), (0,3), and (1,1). And that is indeed the correct answer.
Question 2: By using the transformation y = -f(x-2) on the original points (-3,0), (0,2), and (1,0).
To apply the transformation y = -f(x-2), you need to perform the following steps in the given order: reflection over the x-axis and then a shift right (in the positive x-direction) by 2 units.
Let's go point by point:
For the point (-3,0), start with reflecting over the x-axis. In this case, the y-coordinate changes its sign, so (-3,0) becomes (-3,-0) or simply (-3,0). Next, shift it right by 2 units, resulting in (-3+2,0), which is (-1,0).
For the point (0,2), start with reflecting over the x-axis. The y-coordinate changes sign, so (0,2) becomes (0,-2). After shifting it right by 2 units, we get (0+2,-2), which is (2,-2).
For the point (1,0), reflecting over the x-axis gives (1,-0) or simply (1,0). Shifting it right by 2 units results in (1+2,0), which is (3,0).
Therefore, the transformed points would be (-1,0), (2,-2), and (3,0). Therefore, the correct answer is (-1,0), (2,-2), and (3,0).
Remember, when applying transformations, always follow the correct order of operations, such as reflecting over the x-axis before shifting right.