I missed my math lesson today so I'm struggling on this problem. Can anyone explain? Thanks in advance. :)

Question

Write a rational function to model the situation, or use the given rational function. State a reasonable domain and range for the function using set notation. Then use a graphing calculator to graph the function and answer the question.

 

So far this season, a baseball player has had 84 hits in 294 times at bat, for a batting average of 84/294 which is about 0.286 . How many consecutive hits must the player get to raise his batting average to 0.300?

Answer 1

Hi, Michelle,

 

We can come up with a function to describe the player's average, knowing that the average would be:

 

 

          # of hits       

   # of times at bat

 

So, if the player has already gotten 84 hits out of 294 times at bat, and we assume they get a hit every time they are at bat from now on, their average would be:

 

    84 + x       because each time they are at bat, the number of hits and number of at bats increases by one

   294 + x

 

For the domain of this function, we want to consider what values of x would "make sense" with the problem, and not violate any math rules (like dividing by 0, or having a negative number inside a square root). In this case, it wouldn't "make sense" for x to be a negative number, because if we are just considering the player's future performance, he can't go to bat -2 times, for example. So, the domain would be x = [0,∞). Square bracket on zero because it is a viable number to plug in for x, and infinity always has a round parenthesis.

 

The range (y value) will only get larger as the x value increases, so the range would be [0.286,∞)

 

If you graph this function, you can find how many more at bats/hits (x value) are required to bring the average (y value) to 0.300

 

I hope this helps!