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

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-15=\frac{27.5-15}{10-0}(x-0)$

$y-15=\frac{12.5}{10}(x)$

$y-15=1.25x$

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.

$Domain=\{t|0\leq t\leq 60,t\in W\}$

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

$Range=\{P(t)|15\leq P(t)\leq 90,P(t)\in R\}$

Therefore the correct option is D.

Answer 2

Answer:

NOT B on Edg.

Step-by-step explanation: