Transformations question, please help!!?
Just wanted to make sure I was on the right track.
The question is :
The graph of y = sqrt( a - x ) , a > 0 compared to the graph of y = sqrt(x) has what transformations? Describe in words. What transformations have occurred?
I got horizontal reflection with respect to the y - axis and horizontal translation a units to the right.
- PopeLv 72 months agoFavorite Answer
Yes. Here is how I see it.
Let f(x) = √(a - x).
= √[a - (a - x)]
= f(a - x)
= f[-(x - a)]
The graph of y = √(x) is the graph of y = f[-(x - a)].
Starting from y = f(x), you would effect these transformations in order:
Scale horizontally with respect to the y-axis by factor -1.
Translate by vector <a, 0>.
Those are equivalent to the translations you described.
- Wayne DeguManLv 72 months ago
y = √(-x) is a reflection in the y-axis
y = √(a - x) is a horizontal translation of a units to the left
- 2 months ago
sqrt(x - a) would move it a units to the right (since a > 0)
sqrt(-(x - a)) would flip it horizontally over y = a.
Just graph it out and see it for yourself. Pick some arbitrary value for a and graph all 3 functions
y = x^(1/2)
y = (x - a)^(1/2)
y = (a - x)^(1/2)