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.

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erinna erinna · Answer 1 · 2019-06-27T07:54:24+02:00

Answer:

The correct option is D.

Step-by-step 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

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-15=\frac{27.5-15}{10-0}(x-0)[/tex]

[tex]y-15=\frac{12.5}{10}(x)[/tex]

[tex]y-15=1.25x[/tex]

Add 15 on both the sides.

[tex]y=1.25x+15[/tex]

[tex]P(t)=1.25t+15[/tex]

The family has a budget of $90.

[tex]P(t)\leq 90[/tex]

[tex]1.25t+15\leq 90[/tex]

Subtract 15 from both the sides.

[tex]1.25t\leq 75[/tex]

Divide both sides by 1.25.

[tex]t\leq 60[/tex]

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

[tex]Domain=\{t|0\leq t\leq 60,t\in W\}[/tex]

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

[tex]Range=\{P(t)|15\leq P(t)\leq 90,P(t)\in R\}[/tex]

Therefore the correct option is D.