AnswersFL-1200310-Algebra 1 ASpecial Linear Relationships

Special Linear Relationships Answers

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The pattern of numbers below is an arithmetic sequence:14, 24, 34, 44, 54, ...Which statement describes the recursive function used to generate the sequence?

A
The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14.
B
The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10.
C
The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
D
The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.
2
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The points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. Which statement describes another point on the graph of this function?

A
A 50-page photo album holds 400 photographs.
B
An 80-page photo album holds 560 photographs.
C
A 100-page photo album holds 8,000 photographs.
D
A 900-page photo album holds 8,400 photographs.
3

Which graph represents a function with direct variation?

A
A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).
Option A
B
A coordinate plane with a line passing through (negative 5, 4) and (0, 3).
Option B
C
A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3).
Option C
D
A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).
Option D
4

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

A
y =
Option A
B
y =
Option B
C
y = 7x
D
y = 14x
5

The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass?

A
F = 16.1m
B
F =
Option B
C
F = 32.2m
D
F =
Option D
6

A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served.

Question illustration
A
t = 1.8g
B
t =
Option B
C
g = 1.8t
D
g =
Option D
7

Three points of a function are graphed.

Question illustration
A
The function is a direct variation function with a constant of variation of 1.5.
B
The function is a direct variation function with a constant of variation of 1.8.
C
The function is linear but is not a direct variation function.
D
The function is not a linear function.
8

Which graph represents a function with direct variation?

A
A coordinate plane with a U shaped line graphed with the minimum at (0, 0).
Option A
B
A coordinate plane with a V shaped line graphed with the minimum at (0, 0).
Option B
C
A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).
Option C
D
A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).
Option D
9

Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?

A
–10, –12, –14, –16, –18, ...
B
–2, 8, 18, 28, 38, ...
C
8, 18, 28, 38, 48, ...
D
10, 8, 6, 4, 2, ...
10

The table represents a bicycle rental cost in dollars as a function of time in hours.

Question illustration
A
This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
B
This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.
C
This function does not represent a direct variation because it does not represent the cost for 1 hour.
D
This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.

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