Answers NJ-Algebra I CRRecognizing Patterns

Special Linear Relationships Answers

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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?

F = 16.1m

F =

F = 32.2m

F =

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What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?

k = –

k = –

k =

k =

Three points of a function are graphed.

The function is a direct variation function with a constant of variation of 1.5.

The function is a direct variation function with a constant of variation of 1.8.

The function is linear but is not a direct variation function.

The function is not a linear function.

The graph represents the direct variation function between earnings in dollars and hours worked.

E = 1.5h

E = 7.5h

E = 13h

E = 15h

Which graphs show functions with direct variation? Select three options.

A coordinate plane showing Parking Garage Rates with Time in hours on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2.4) and (5, 4).

A coordinate plane showing Cost of Cinnamons with Quantity in ounces on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 0.3) and (5, 1.5).

A coordinate plane showing Breakfast Cost with Number of Meals on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 1.2) and (5, 6).

A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1, 2) and (5, 8).

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

y =

y = 7x

y = 14x

Which graph represents a function with direct variation?

A coordinate plane with a U shaped line graphed with the minimum at (0, 0).

A coordinate plane with a V shaped line graphed with the minimum at (0, 0).

A coordinate plane with a line passing through (negative 4, 2), (0, 0) and (4, negative 2).

A coordinate plane with a line passing through (negative 2, negative 3), (0, 1) and (1, 3).

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

–10, –12, –14, –16, –18, ...

–2, 8, 18, 28, 38, ...

8, 18, 28, 38, 48, ...

10, 8, 6, 4, 2, ...

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?

The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14.

The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10.

The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.

The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.

The sequence below shows Marisa’s library fine starting on the first day her book is overdue and for each additional day afterward:$0.50, $0.65, $0.80, $0.95, $1.10, ...Let f(n) represent Marisa’s library fine (in dollars), where n is the number of days the book has been overdue, starting with n=1 for the first day overdue.Which equation represents Marisa’s library fine as a function of a book that is n days overdue?

f(n) = 0.15n

f(n) = 0.50n

f(n) = 0.15n + 0.35

f(n) = 0.50n + 0.15

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