Question

The function g results when the graph f(x) = √x is reflected over the x-axis and horizontally stretched by a factor of 3. Which equation describes the function g?

-g(x) = -√(x/3)
-g(x) = -√(3x)
-g(x) = √(x/3)
-g(x) = -1/3 √x

Answer 1

I know since it's reflected over the x-axis there has to be a negative in front, so that eliminates g(x) = √(x/3)
The stretch and shrink is what is giving me trouble. In this case it's a horizontal stretch, so if I'm mistaken that means it'll be f(√x/3)

My answer is: g(x) = -√(x/3)

Correct me if I'm wrong sir.

Answer 2

almost. To shrink horizontally, multiply
g(x) = -√(3x)
think about it. As x increases, 3x increases three times a fast, thus compressing the graph.

In general, to scale by a factor of m, replace x by x/m or y by y/m

You can see that in the case of y, that means
y/m = f(x)
so y = m*f(x)
and that stretches the graph vertically.

so to scale x by a factor of 1/3, replace x by x/(1/3) = 3x