Question

Evaluate the floor functions for the given value.

f(x) = 2⌊x⌋; g(x) = ⌊2x⌋; x = 1.2


Are the two values the same?


A. yes; f(1.2) = 2, g(1.2) = 2

B. yes; f(1.2) = 2.4, g(1.2) = 2.4

C. no; f(1.2) = 2, g(1.2) = 3

D. no; f(1.2) = 3, g(1.2) = 2


Pleaseeee help and it is not C nor D

Answer 1

The floor function is where we round down to the nearest integer. It does not matter how close we are to the ceiling. We always round down. I recommend drawing a vertical number line.

A few examples:

• Floor(0.00372) = 0
• Floor(1.2) = 1
• Floor(1.7) = 1
• Floor(1.99) = 1
• Floor(1.9999999) = 1

Let's now plug x = 1.2 into each f(x) and g(x) function.

f(x) = 2*floor(x)

f(1.2) = 2*floor(1.2)

f(1.2) = 2*1

f(1.2) = 2

and,

g(x) = floor(2x)

g(1.2) = floor(2*1.2)

g(1.2) = floor(2.4)

g(1.2) = 2

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We conclude that f(1.2) = 2 and g(1.2) = 2

Answer: Choice A