Constructing Functions from Tables Warmup

What is the rule in this table?

• Multiply the number of days by 7 and add 1

• Add 7 to the number of days

• Multiply the number of days by 4 and add 4

• Add 13 to the number of days

Answer explanation

The correct rule is to multiply the number of days by 7 and add 1. This aligns with the pattern observed in the table, where each value corresponds to this calculation.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Write an equation in y = mx + b form for the cost, y, to belong to the gym for x months.

• y = 35x + 40

• y = 40x + 35

• y = 35 x + 70

• y = 75x

Answer explanation

The equation y = 35x + 40 represents a monthly cost of $35 for gym membership plus a one-time fee of $40. This matches the format y = mx + b, where m is the monthly rate and b is the initial cost.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Write the function for the following table:

• f(x)= 1(2)^x

• f(x)= 2(1)^x

• f(x) = 2x+1

• f(x)= x+2

Answer explanation

The function f(x)=1(2)^x represents exponential growth, which matches the table's pattern of increasing values. The other options either represent linear functions or constant values, making them incorrect.

Tags

CCSS.HSF.LE.A.2

Write the function for the following table:

• f(x) = 4x+5

• f(x)= 4x+1

• f(x)= 1(4)^x

• f(x)= 5(4)^x

Answer explanation

The function f(x) = 4x + 1 correctly represents a linear relationship where the slope is 4 and the y-intercept is 1, matching the values in the table. The other options do not fit the linear pattern.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Write the function for the following table:

• f(x) = 1(3)^x

• f(x) = 3(3)^x

• f(x) = 3x+3

• f(x)= 6x+1

Answer explanation

The function f(x) = 1(3)^x represents exponential growth, matching the table's pattern. The other options are either linear or have incorrect coefficients, making f(x) = 1(3)^x the correct choice.

Tags

CCSS.HSF.LE.A.2

Write the function for the following table:

• f(x) = 5x + .08

• f(x)= 5x + 2

• f(x) = .08(5)^x

• f(x)= 2(5)^x

Answer explanation

The function f(x) = 2(5)^x matches the exponential growth pattern indicated in the table, where the output increases rapidly as x increases, confirming it as the correct choice.

Tags

CCSS.HSF.LE.A.2