To determine which function correctly represents how much taller Justin's plant is compared to Kira's plant [tex]\( x \)[/tex] weeks after transplanting, we need to find the difference between the heights of the two plants.
The function [tex]\( j \)[/tex] for Justin's plant is given by:
[tex]\[ j(x) = 18 + 6x \][/tex]
The function [tex]\( k \)[/tex] for Kira's plant is given by:
[tex]\[ k(x) = 12 + 4x \][/tex]
To find how much taller Justin's plant is than Kira's plant, we need to calculate [tex]\( (j - k)(x) \)[/tex], which is the difference between the two functions:
[tex]\[ (j - k)(x) = j(x) - k(x) \][/tex]
Substitute the expressions for [tex]\( j(x) \)[/tex] and [tex]\( k(x) \)[/tex] into the equation:
[tex]\[ (j - k)(x) = (18 + 6x) - (12 + 4x) \][/tex]
[tex]\[ (j - k)(x) = 18 + 6x - 12 - 4x \][/tex]
[tex]\[ (j - k)(x) = (18 - 12) + (6x - 4x) \][/tex]
[tex]\[ (j - k)(x) = 6 + 2x \][/tex]
Therefore, the function representing how much taller Justin's plant is than Kira's plant [tex]\( x \)[/tex] weeks after transplanting is:
[tex]\[ (j - k)(x) = 6 + 2x \][/tex]
The correct answer is:
A. [tex]\( (j - k)(x) = 6 + 2x \)[/tex]
