Vasumathi N. answered • 04/05/21
Effective Math Tutor . Cater to Various Learning Styles.
Question - Does it matter which translation must be done first?
You have more than one translation to do. Just like in any math problem, when you have more than one operation to perform you would use the Order of Operations, in this problem also you have to follow the correct sequence of translations. Here is the sequence to follow:
First, do what is inside the parenthesis - Horizontal shift Left/Right , let's say b
Next is Multiplication - Stretch/Compression , say a
Last is Addition or Subtraction - Vertical Shift Up/Down , say c
In general, g(x) = a f(x ± a) ± c
My questions to you:
What does the value of a look like for (i) Stretch? (ii) compression?
Horizontal shift- when is it +, when is it - ?
I want you to have fun with this problem- grab a graph paper at least 2 color pencils, change the order of translation and see what happens!
Vasumathi N.
Ok. Based on the way I described the sequence , Horizontal shift first. So, the x in f(x) changes to x+1. Next we deal with the Compression. So , now we have (1/2)(x+1). Last comes the vertical shift. So now we have g(x) = (1/2)(x+1)-4. Let us simplify. So now we have g(x) =(1/2)x +(1/2) - 4. which further simplifies to g(x) = (1/2)x - (7/2). As you can see now, g(x) is a linear function with the slope =1/2 . Remember that y intercept is the value of y when x=0. So, substitute x=0 in the final equation for g(x) and you will see that y-intercept = -7/2 . Now suppose, you follow the sequence as it appears in your question, then the result is as follows: First apply vertical compression of 1/2. so f(x) =x changes to a new f(x)=(1/2)x Next apply a shift left by 1. so now, we have a newer f(x) = (1/2)x +1 . Lastly, apply a shift of down by 4. So now we have g(x) = (1/2)x +1 -4. Can be simplified to g(x) = (1/2)x -3. In this case ,slope = 1/2 and the y-intercept = -3 Moral of the story- 1.If i am in your Precalc class, I will check my class notes, lecture notes, look at examples worked by my instructor in the class to see what was the approach used. If I did not find the information, I will reach out to the instructor to explore further. 2. Keep the resulting function in the most simplified form to identify the slope and the intercept. This was indeed a great problem leading to an interesting discussion. Please let me know and ask a specific question if you did not understand any part of this discussion. I will be glad to explore it further.04/06/21
Katelyn J.
I still don’t understand04/06/21