A rubber bouncy ball is bouncing up and down such that the ball's distance, d, in feet above the ground is given by the inequality Which of the following graphs shows all the possible distances?

Option D.

Step-by-step explanation:

We have the inequality:

Id - 3.5I ≤ 1.5

remember that : IxI < d means that:

-d < x  < d

Now let's find the possible values of d, breaking the absolute value we have that:

-1.5 ≤ d - 3.5 ≤ 1.5

adding 3.5 in each part, we have:

-1.5 + 3.5 ≤ d - 3.5 + 3.5 ≤ 1.5 + 3.5

2 ≤ d ≤ 5

Then d can be any value in the set [2, 5]

Then the correct graph is D, because the purple line starts at 2, and ends at 5.

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2