Answer: Choice B
g(x) = -f(x) - 4
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Step-by-step explanation:
The point (0,1) is on the the red f(x) curve. It's the y-intercept.
If we reflected that point over the x axis, then it moves to (0,-1). Shift it down 4 units to get to (0,-5)
The point (0,-5) is on the purple g(x) curve.
This process of...
- reflect over the x axis
- shift down 4 units
is applied to every point on the red curve to arrive at a corresponding point on the purple curve. The order of the transformations matters. We can't shift down first before reflecting (or else g(x) will be in a different spot).
We stick a negative sign in front of the f(x) to reflect over the x axis. This is to change the sign of the y coordinate from positive to negative. Our answer choices are narrowed to either B or C.
The answer is choice B since that -4 at the end means "shift each point 4 units down". We're subtracting 4 from each y coordinate.
GeoGebra and Desmos are two useful tools to help verify the answer.