Final answer:
The linear functions among the given options are f(x) = 4(2+3x) + 3, which simplifies to a linear equation, and f(x) = 1, which represents a horizontal line with a slope of zero.
Step-by-step explanation:
To identify the linear function out of the given options, we need to look for an equation that can be expressed in the form y = mx + b, where m and b are constants, and m is the slope of the line.
The first option f(x) = 4(2+3x) +3 simplifies to f(x) = 4×2 + 4×3x + 3 = 8 + 12x + 3 = 12x + 11, which is a linear equation.
The second option f(x) = 1 is also a linear equation, representing a horizontal line with a slope of zero.
The third option f(x) = 5 - 2³ is not a function of x and therefore not linear.
The last option is approximately written and the function it describes is not completely clear.
Out of the clear and complete options, the first option and the second option represent linear functions.