Question

Will someone evaluate my answers and guide me through answering the last two parts of the problem? Thank you.

5. Principal Farley has $200 to pay for some teachers to attend a technology conference. The company hosting the conference is allowing 2 teachers to attend for free. The number of teachers y that can be sent to the conference is given by the function y = 200/x + 2, where x is the cost per teacher.

a. Describe the reasonable domain and range values for this function.
b. Identify the vertical and horizontal asympototes.
c. Graph the function.
d. Give two points on the graph whose coordinates are whole numbers and describe what they mean in the context of the situation.

My answers:

a. A reasonable range is x = 25 to 200, y = 1 + 8 (all real numbers).

b. Vertical: x = 2; horizontal: y = 0.

c. ?

d. ?

Answer 1

a. x must be greater than 0 (undefined for x = 0) so x = 0 is not in the domain (infinite number of teachers)
y, must be greater than 2 so range is 2 to very large (for small cost per teacher.) If x is a dollar per teacher, then y = 202 which seems a reasonable upper limit.

b. Vertical where x = 0 as explained in a above. Horizontal as x gets very big y --->2 (can only send the 2 free teachers)

c. I can not graph this for you. Pick a few values of x within the domain and compute y