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.

Relevance
• Pope
Lv 7
2 months ago

Yes. Here is how I see it.

Let f(x) = √(a - x).

√(x)

= √[-(-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.

• 2 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)

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)