Question

The table represents the total price including parking, p(t), for family fair packages with various numbers of included tickets, t. If a family has a budget of $90, what are the restricted domain and range of the function? T= 0 10 20 30 40 50. P(T)=15 27.5 40 52.5 65 77.7

A. The domain is restricted to all whole numbers from 0 and 50 inclusive. The range is all real numbers from 0 to 77.5 inclusive. B. The domain is restricted to all whole numbers from 0 and 50 inclusive. The range is all real numbers from 15 to 77.5 inclusive. C. he domain is restricted to all whole numbers from 0 and 60 inclusive. The range is all real numbers from 0 to 90 inclusivTe. D. The domain is restricted to all whole numbers from 0 and 60 inclusive. The range is all real numbers from 15 to 90 inclusive.

Answer 1

The correct option is D.

Explanation:

It is given that the table represents the total price including parking, p(t), for family fair packages with various numbers of included tickets, t.

t : 0 10 20 30 40 50

P(t) : 15 27.5 40 52.5 65 77.7

Choose any points from the table. (0,15) and (10,27.5).

The equation of function is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-15=(27.5-15)/(10-0)(x-0)`

`y-15=(12.5)/(10)(x)`

`y-15=1.25x`

Add 15 on both the sides.

`y=1.25x+15`

`P(t)=1.25t+15`

The family has a budget of $90.

`P(t)\leq 90`

`1.25t+15\leq 90`

Subtract 15 from both the sides.

`1.25t\leq 75`

Divide both sides by 1.25.

`t\leq 60`

Domain is the set of inputs or the values of t.

`Domain=\t`

Range is the set of outputs or the values of function p(t).

`Range=\P(t)`

Therefore the correct option is D.