Determine the more basic function that has been shifted, reflected, stretched, or compressed.

Question

w(x)=(√-x)-4

Step 1 of 2 :  

Determine the more basic function that has been shifted, reflected, stretched, or compressed.

Answer 1

w(x) = sqrt(-x) - 4 (the given function)

The idea behind these transformation questions is to first find the basic parent function hiding inside, and then read off what has been done to it. Every square root function is built from the same parent:

f(x) = sqrt(x) (the basic function)

Now lets look at what has been changed in w(x):

sqrt(-x) The x inside the square root became -x, which reflects the graph across the y-axis

1. 4 Subtracting 4 at the very end shifts the whole graph down 4 units

There is no number multiplying the square root and no number multiplying the x inside it, so there is no stretch or compression here.

So, w(x) is the basic function sqrt(x), reflected across the y-axis and then shifted down 4 units.

Something worth remembering is that changes INSIDE the square root affect x, so they are horizontal and they do the opposite of what they look like. Changes OUTSIDE the square root affect y, so they are vertical and they do exactly what they look like.

Lastly, we can find the domain, since the inside of a square root cannot be negative:

-x >= 0 Multiply both sides by -1 and flip the inequality

x <= 0

So the domain is x <= 0. And since sqrt(-x) is always 0 or greater, the smallest w(x) can be is -4, which makes the range y >= -4.

Basic function: f(x) = sqrt(x)

Answer 2

Base function

w(x) = x