Question

PLEASE ANSWER THIS ITS VERY IMPORTANT

The function f(x) = x + 5 represents the number of animals adopted at one shelter, where x is the number of months.



The function g(x) = 4x + 7 represents the number of animals adopted at another shelter, where x is the number of months.



Part A: What is (f + g)(x)? Show all necessary steps. (2 points)



Part B: Evaluate (f + g)(4). Show your work. (2 points)



Part C: Explain what your answer represents in terms of the scenario. (2 points)

Answer 1

Explanation:

Part A: To find (f + g)(x), we need to add the functions f(x) and g(x) together.

f(x) = x + 5

g(x) = 4x + 7

To add the two functions, we simply add the corresponding terms:

(f + g)(x) = (x + 5) + (4x + 7)

= x + 5 + 4x + 7

= 5x + 12

Therefore, (f + g)(x) = 5x + 12.

Part B: To evaluate (f + g)(4), we substitute x = 4 into the expression for (f + g)(x):

(f + g)(4) = 5(4) + 12

= 20 + 12

= 32

Therefore, (f + g)(4) = 32.

Part C: The expression (f + g)(x) represents the total number of animals adopted at both shelters combined, where x is the number of months. The coefficient of x, which is 5, represents the rate of increase in the number of animals adopted each month when both shelters are considered together. The constant term, which is 12, represents the initial number of animals adopted when x is 0.

In the scenario, if we evaluate (f + g)(4), which is 32, it means that after 4 months, a total of 32 animals have been adopted at both shelters combined.