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Leveled PracticeIn6–7, explain whether each graph represents a function.

A line rises from approximately (0, 10) through approximately (5, 70).
A curve rises from approximately (0, 10) through estimated points (2, 20) and (4, 90).
Hannah approximates the areas of circlesusing the equationmath
A
=
3
r
2
,
and records areasof circles with different radius lengths in a table.



Radius (in.)

1

2

3

4

5

Area (in.2)

3

12

27

48

75

a.Graph the ordered pairs from the table.

b.Is the relation a function? Explain.

A coordinate plane has radius in inches on the horizontal r-axis from 0 to 8 in increments of 1 and area in square inches on the vertical A-axis from 0 to 80 in increments of 10.
Model with MathThe relationship betweenthe number of hexagons,x, and the perimeterof the figure they form,y, is shown in thegraph. Is the perimeter of the figure a functionof the number of hexagons? Explain.

A graph of perimeter, y, versus number of hexagons, x, has points plotted in an apparent line, at approximately (1, 12), (2, 20), (3, 28), and (4, 36).
Construct ArgumentsDo the ordered pairsplotted in the graph below represent a function?Explain.

A graph has points plotted at (negative 5, 0), (negative 4, negative 4), (negative 3, negative 4), (negative 1, 0), (4, 3), and (4, negative 3).

Answers

Answered by GPT-5 mini
Here are answers and brief explanations.

1) Leveled Practice (In 6–7)
- Graph 1 (line from about (0,10) through (5,70)): Yes — it passes the vertical line test (each x has one y).
- Graph 2 (rising curve through (0,10), (2,20), (4,90)): Yes — again each x corresponds to a single y, so it is a function.

2) Hannah’s circle areas
a. Ordered pairs: (1, 3), (2, 12), (3, 27), (4, 48), (5, 75). (These lie on A = 3r^2.)
b. Is it a function? Yes — each radius (input) gives exactly one area (output), so the relation is a function.

3) Model with Math (hexagons)
- Yes. The plotted points (1,12), (2,20), (3,28), (4,36) show one y for each x, so perimeter is a function of the number of hexagons. (Pattern: y increases by 8 each time; y = 8x + 4 fits these points.)

4) Construct Arguments
- The set {(−5,0), (−4,−4), (−3,−4), (−1,0), (4,3), (4,−3)} is NOT a function because x = 4 corresponds to two different y-values (3 and −3), failing the vertical line test.
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