The order you do a transformation matters. Answer all the questions.
Let's say we have the function f(x) = x^2. Let's put it through the following transformations.
a. translate up 2
b. reflect over the x-axis.
1. What would the graph look like if you did 'a' first and then 'b'?
2. What would the graph look like 'b' first and then 'a'
3. Make a prediction of what g(x) = (-x - 2)^2 is going to look like.
4. Double check in your calculator. How can you explain your findings?
(If you do not have a graphing calculator on you, you can go to http://webgraphing.com/graphing_basic.jsp)
Jessica Revolorio
ReplyDeleteGraphs 1 and 2 are going to look exactly the same so it wouldn't matter in what order you do the transformations.
Image: Parabola frowning down, up two units
Graph 3
image: Parabola reflected on the y-axis, transformed to the right two units
For question 1 and 2, the graphs would look exactly the same. There would be no difference at all no matter which one you did first.
ReplyDeleteFor question 3 and 4 the graph would be a Parabola that is reflected over the y-axis and translated two units to the right. But as I checked on the calculator, it was actually translated two units to the left. I think it went to the left and not the right because the ^2 part of the graph made (x-2) to (x+2) causing it to move left.
1 and 2
ReplyDeleteThe graph would look the same whether you did a first or b first. This is because addition and multiplication are commutative. They both would be a parabola pointing up with the middle point at (0,2)
3
A parabola reflect over y-axis and 2 units to the right.
uhhh... i dunno if i messed up some where but every time i work it out i get the same answer so... lets see... I cant really say i agree with the comments above about questions 1 and 2... because,the parabola's "vertex" would be at (0,0) without translations, after shifting upwards 2 units, we are now at (0,2)... after reflecting over the X-axis, we end up at the point (0,-2)(due to the reflection) but if we did B first, we would being at (0,0) then after reflection, we would still be at (0,0). Then after shifting up 2 units, we end up at (0,2) =P stop me if I'm wrong
ReplyDeleteand for questions 3 and 4, I said it was a parabola shifted to the left 2 units, because even though the translation tells us to shift to the right 2 units (due to the -2 being on the inside with X) the translation ALSO says to make sure that after that, we reflect across the Y axis making the shift OPPOSITE of what we were originally told.
ReplyDelete1. If I did 'a' first and then 'b', the parabola would be up 2 units but then flipped over facing down.
ReplyDelete2. If I did 'b' first and then 'a', the graph would be the exact same thing as i did for #1, just in a different order. There's no difference.
3. My prediction is that since it's -x, it will be reflected over the y-axis. Then since -x - 2 is in paranthesis, the parabola would move to the right 2 units. If it's in the parenthesis, it goes the opposite way. The parabola would look like -x^2, shifted 2 units to the right.
For the 1st and 2nd graph there would be no change its hust in a different order.
ReplyDeleteIn graph 3 the parabola would go 2 units to the right because of the ^2
1.i move up 2 then flipped over the x axis
ReplyDelete2. i flipped over the x axis then move up 2. then the graph will look the same we just did the graph in different order.
3, the graph would slightly move to the right from the original graph and it would flipped over y axis
For questions 1 and 2 they are going to look the same because it's the same function but you are just doing them in different order.
ReplyDelete3. its going to reflect on the y-axis and translates to right 2.
4.when i did it on my calculator the graph would move to the left instead of the right,so i am kind of confused because whenever a number would be in the parenthesis for example (x-2) the graph would move to the right 2 and when the number would be positive the graph would go to the left 2, but in this case it just went to the left when the 2 was negative so i don't know.
Questions 1 and 2: Graphs would be the same, It doesn't matter what order they are in.
ReplyDeleteQuestion 3: The graph would be reflected over the y-axis and it would be a parabola, and it will also translate two units to the right, since the 2 is on the outside; it will go right or left. The two is positive so that's why it goes right. If it was negative then it would go left.
Question 4: The graph was shifted to the left not the right..which was odd.
Question 1. The graph would be reflected over the x-axis and the translation would be 2 units down(y-intercept)
ReplyDeleteQuestion 2. The graph would be reflected over the x-axis but the translation would be two units up to find the y-intercept.
Question 3. The graph would be reflected over the y-axis after the translation of 2 units to the right.
1. The function would be flipped over the x axis and the y intercept would be at -2.
ReplyDelete2. The function would be flipped over the x axis and the y intercept would be at 2.
3. The graph would be a parabola and it would be reflected over the y axis and slide 2 units right
For questions 1 and 2 the graph would look like flipped. Facing down. And up 2 units.
ReplyDeleteg(x) = (-x - 2)^2= the graph would be reflecting over the y-axis and 2 units to the right. And then it would be a parabola because of the ^2.
(LATE) :(