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

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.

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

Why did the function go see a therapist? Because it needed some reflection and stretching in its life! Okay, let's get to the answer. When the graph of f(x) = √x is reflected over the x-axis, it becomes -√x. And when it's horizontally stretched by a factor of 3, it becomes √(3x). So, the equation that describes the function g is: -g(x) = -√(3x). Keep stretching and reflecting, my friend!

To determine the equation describing the function g, which is the result of reflecting the graph of f(x) = √x over the x-axis and horizontally stretching it by a factor of 3, we need to understand the transformations involved.

First, reflection over the x-axis: This transformation is achieved by multiplying the function by -1. So, the negative of f(x) = √x is -√x.

Next, horizontal stretch by a factor of 3: In this case, we need to divide the x-values by 3 to horizontally stretch the function. This stretching formula affects the x-coordinate, but does not impact the y-coordinate.

Combining these two transformations, we get the equation for g(x): -√(x/3). Therefore, the correct equation that describes the function g is:

-g(x) = -√(x/3)