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Integrated math 3

Course: Integrated math 3>Unit 6

Lesson 1: Shifting functions

Graphing shifted functions

Given the graph of f(x)=x², Sal graphs g(x)=(x-2)²-4, which is the graph of f shifted 2 units to the right and 4 units down.

Want to join the conversation?

• Why does Sal move the graph 2 units to the right when it says -2 at ?

Shouldn't he move it to the left by 2 units?
• Think about it on a coordinate plane: if I shift 0 two to the right, I get 2. Because you have to think about it in terms of 0, not 2, you subtract 2 instead of adding 2.
• I wish these videos were explained better. I feel like its really brief and I still don't understand how you get to where you are by the end. I wish I could be more specific but I guess I don't understand it. There is no introduction really explaining whats going on either. Also taking the simplest explanation and then jumping to advanced problems there is no bridge.
• My favorite video about this topic is the Shifting Functions Introduction video. I love how Sal explains this concept there.
• Does the fact that the x-2 is squared change the graph? Why not?
Also, is f(x)=x the same thing as f(x)=x^2? Why or why not?
• Anyone besides me have trouble with the interactive graphs? On the quiz after "Shifting Functions" I bet I took the quiz four times to even get three out of four correct. And each time I know I had the formula for shifting graphs figured out correctly but when I graphed the functions with the interactive graphs I got each one wrong. And I believe it was a result of me not being able to set the graphs exactly right. For example, the last graph I tried the tip of the graph was 8 places to the right and one place up. And when I set the graph to that location the system still counted it wrong. In the answer it said shift the tip of graph four places right and one place up.

Any suggestions?

Fred Haynes
• Hmm I see your problem. In order to graph a function, you have to have it in vertex form;

a(x-d)² + c <---- Basic Form

Example: (x-3)² + 3
Since there's no a, you don't have to worry about flipping on the x axis and compressing or stretchign the function. Now we look at d. d = -3. In order to find the zeros of the function, x must equal 3. That's why the equation moves to the right when d is negative and when d is positive, the equation moves to the left. So simply to say, (x-d)² = 0 When you know d, then your x will be something that subtracts d to equal 0. So in this example, the function shifts 3 units to the right. Now we look at c. c is 3, which means that the graph moves 3 units up. And voila! There you have it! If you need more clarification, don't hesitate to ask. I hope this helped!
• At , This logic about shifting the x to the right when g(x)=(x-2)^2 -4 is on the graph, doesn't make any sense to me?
"Turn RIGHT to go LEFT? yes! Thank you! or should I say no thank you? Cause in opposite world maybe that really means thank you!" - Lightning McQueen

I need an explanation... Thank you! :D
• think about it this way: you start with y=x^2 which goes through (0,0). So if you have y=(x-2)^2, what value of x is needed so that y will be 0 (still the x intercept)? so if you put x=2, you get the point (2,0) which is 2 to the right. If you have y=(x+2)^2, x has to equal -2 to give the point (-2.0) and thus is a shift to the left.
• Why x-2 needs to be zero when x=2? Why do we want to square zero?
• If you are subtracting a number from x, wouldn't that shift it to the left since it would decrease the value of x?
• Think of the equations: g(x)=x and f(x)=x-1. The same value of g(x) and f(x) will be made by an x value one greater in the function f than the x from the function g . Therefore, the graph will move to the right.
• In the subsequent practice section, the term 'transformation' is used, not shift. I assume every shift is a transformation, but is every transformation a shift?