Question

understand and graph functions
use the information to answer problems 1–3.
mrs. dubois is planning a fruit cup party for a class of 18 students and two teachers. she spends $10 for a package of snacks and also takes orders in advance for fruit cups that cost $3 each.

1. describe the domain of the function both in words and numbers.

1. what is the range of the function?

1. plot the data shown in the table on the coordinate plane. if the data are continuous, draw a solid line through the plotted points.

fruit cup orders	0	5	10	15	20

(graph with x - axis: fruit cup orders, y - axis: total cost ($), with scales 0,10,20 on x and 0,10,20,30,40,50,60,70 on y)

use the graph to answer problems 4–5.

1. construct arguments does the graph represent a function? explain.

(graph with x from 0 - 10, y from 0 - 10, with a curved line having loops)

1. name a section of the graph that, taken in isolation, is a function.

1. open ended draw a graph that does not represent a function.

(graph with x from 0 - 10, y from 0 - 10, blank for drawing)

Explanation:

Step1: Define domain (words/numbers)

Words: The number of fruit cup orders (non-negative integers, up to a reasonable maximum for 18 students + 2 teachers, so 0 to 20 as given, or all non-negative integers where orders make sense for the group).
Numbers: $\{0, 5, 10, 15, 20\}$ (discrete values from the table; can also be all integers $0 \leq x \leq 20$ since partial orders don't make sense)

Step2: Identify range from table

Extract cost values from the table.
Range values: $\{10, 25, 40, 55, 70\}$

Step3: Plot points (summary)

Plot coordinates: $(0,10), (5,25), (10,40), (15,55), (20,70)$. Since you can't order partial fruit cups, the data is discrete, so no solid line.

Step4: Test function for graph 4

Apply vertical line test: A vertical line intersects the graph at more than one point (the loops), so it fails.

Step5: Identify valid function section

Choose a section where no vertical line intersects more than once, e.g., the leftmost segment from $x=0$ to $x=3$.

Step6: Draw non-function graph

Create a graph that fails the vertical line test, e.g., a vertical line $x=5$, or a circle $x^2 + y^2 = 25$.

Answer:

1. Domain (Words): The number of fruit cup orders (non-negative whole numbers, from 0 up to 20, since that covers the possible orders for the group).

Domain (Numbers): $\{0, 5, 10, 15, 20\}$ (or all integers where $0 \leq x \leq 20$)

1. Range: $\{10, 25, 40, 55, 70\}$
2. (Plotted points: $(0,10)$, $(5,25)$, $(10,40)$, $(15,55)$, $(20,70)$; no solid line, as data is discrete)
3. No, the graph does not represent a function. It fails the vertical line test: a vertical line drawn through the loops will intersect the graph at more than one point, meaning one $x$-value maps to multiple $y$-values.
4. The segment of the graph from $x=0$ to $x=3$ (any segment where a vertical line only intersects the graph once is valid).
5. (Example graph: A vertical line $x=5$, or a circle centered at the origin with radius 5, which fails the vertical line test.)