Question

Which scenario could cross the x-axis more than once if x is the number of times Jon kicks the ball and y is the number of points he scores?

Jon earns 2 points for every goal he gets, but loses 1 point for every goal he misses.

Jon earns 2 points for every goal he gets.

To warm-up, Jon kicks the ball several times before the scorekeeping begins.

Jon's older brother gives him a head-start with a few points before the game starts.

Answer 1

Jon earns 2 points for every goal he gets, but loses 1 point for every goal he misses.

Answer 2

i.e. the first option.

Answer 3

Thank you:)

Answer 4

Do you want to know why the first option is correct?

Answer 5

Yes please :)

Answer 6

For a function to cross the x-axis, first it has to go to the positive area of the graph or the negative.

Answer 7

That rules out "To warm-up, Jon kicks the ball several times before the scorekeeping begins."

Answer 8

If Jon never gets any points, then the function STAYS ON the x-axis, but never CROSSES it.

Answer 9

Then, the function has to go to the other area of the graph.

Answer 10

So, that also rules out "Jon's older brother gives him a head-start with a few points before the game starts.", because I am assuming that Jon never scores any points in this scenario.

Answer 11

It also rules out "Jon earns 2 points for every goal he gets.", because Jon starts out with 0 points, gets some, but never loses any, so can't get negative total points.

Answer 12

Got it! :)

Answer 13

Thanks, and you're welcome! Do you need any more help?