The junior and senior class officers are sponsoring a homecoming dance. the total cost for the facilities and catering is $45 per person plus a $2500 deposit. write and graph an equation to represent the average cost per person. then explain any limitations to the domain and range.

Domain is (0,∞)

Range is (45, ∞)

Step-by-step explanation:

Let x represents the number of persons and f(x) represents the average cost per person,

∵ Fixed cost = $ 2500

Also, additional cost is $ 45 per person,

So, the total cost for x persons ( in dollars ) = fixed deposit + additional cost for x persons,

= 2500 + 45x

Which is a rational function,

∵ A rational function is defined for all real numbers except those for denominator = 0

Denominator of f(x) = x

So, f(x) is defined for all real numbers except x ≠ 0,

Now, the cost can not be negative,

⇒ x > 0

Hence, the domain for f(x) is (0, ∞)

Again,

If

So, 45 < f(x) < ∞

i.e., range of f(x) is (45, ∞)

70.30

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: