Question

select the correct answer. justin and kira use functions to model the heights, in centimeters, of two sunflower plants x weeks after transplanting them to the school garden. function j models the height of justins plant: j(x) = 18 + 6x. function k models the height of kiras plant: k(x) = 12 + 4x. which function correctly represents how much taller justins plant is than kiras plant, x weeks after they were transplanted to the school garden? a. (j - k)(x) = 30 + 10x b. (j - k)(x) = 6 + 2x c. (j - k)(x) = 6 + 10x d. (j - k)(x) = 30 + 2x

Explanation:

Step1: Recall function subtraction

To find how much taller Justin's plant is than Kira's, we need to compute \((j - k)(x)\), which is \(j(x)-k(x)\).

Step2: Substitute the functions

We know \(j(x) = 18 + 6x\) and \(k(x)=12 + 4x\). So, \((j - k)(x)=j(x)-k(x)=(18 + 6x)-(12 + 4x)\).

Step3: Simplify the expression

First, distribute the subtraction: \(18 + 6x-12 - 4x\). Then, combine like terms: \((18 - 12)+(6x - 4x)=6 + 2x\).

Answer:

B. \((j - k)(x)=6 + 2x\)