In a free throw shooting contest, you shoot free throws until you miss once or until you make four shots. you keep track of the sequence of misses/makes. how many outcomes are in the sample space for this experiment?

5 outcomes.
Let 0 being misses and 1 being makes.
The first outcome is 0, which is a miss.
The second outcome is 1,0, which is first a make, then a miss
The third outcome is 1,1,0, which is first a make, the next one being a make, and the final one being a miss.
The fourth outcome is 1,1,1,0, which is first a make, the second one being a make, the third one being a make, and the fourth one being a miss.
The final outcome is 1,1,1,1, which is every shot is a make.

The correct answer would be the function g(x) increased at a faster rate