Question

Isaac orders dried fruit from an online health food store. He pays a price per pound for the fruit, and a flat shipping fee. This table shows the total cost for different amounts of fruit ordered.What is the most reasonable domain and range for the situation?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Using a linear function, it is found that:

• A reasonable domain is: $x \in (0, \infty)$.
• A reasonable range is: $y \in (10, \infty)$

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A linear function has the following format:

$y = mx + b$

In which:

• m is the slope, which is the rate of change.
• b is the y-intercept, which is the value of y when x = 0.

• Two points (x,y) on the table are: (0.5, 14) and (0.75,16).
• The slope is given by change in y divided by change in x, thus:

$m = \frac{16 - 14}{0.75 - 0.5} = \frac{2}{0.25} = 8$

Thus

$y = 8x + b$

Point (0.5, 14) means that when $x = 0.5, y = 14$, and we use it to find b.

$y = 8x + b$

$14 = 8(0.5) + b$

$b = 10$

The function is:

$y = 8x + 10$

• The domain of a function is the set that contains all possible input values.

• In this problem, the input is the amount of pounds of fruit that is ordered, which is a positive value greater than 0. Thus, the domain is $x \in (0, \infty)$.

• The range of a function is the set that contains all possible output values.
• In this problem, the output is the cost. Linear function in which when $x = 0, y = 10$, thus, the cost will always be greater than 10, which means that the range is: $y \in (10, \infty)$.

A similar problem is given at https://brainly.com/question/10891721