Question

The function f(x) = 9x + 27 represents the distance in miles a drone flew. The function g(x) = x + 3 represents the time the drone flew in hours. Part A: Find f(4) and g(4). Show your work. (2 points) Part B: Find f divided by g of 4. Show your work. (2 points) Part C: What is the domain of f divided by g of x? (2 points)

Answer 1

Explanation:

Part A: f(4) = 63, and g(4) = 7.

My work for Part A:

Step 1: Write the first function substituting x for 3: f(4) = 9 x 4 + 27.

Step 2: Solve the function: f(4) = 9 x 4 = 36, and 36 + 27 = 63.

Step 3: Write the final answer for the first function: f(4) = 63.

Step 4: Write the second function substituting x for 3: g(4) = 4 + 3.

Step 5: Solve the function: g(4) = 4 + 3 = 7.

Step 6: Write the final answer for the second function: g(4) = 7.

Part B: (f/g)(4) = 9.

My work for Part B:

Step 1: Using the numbers from Part A, simply divide f(4) by g(4) to get (f/g)(4): 63/7 = 9.

Step 2: Write the final answer of (f/g)(4): (f/g)(4) = 9.

Part C: The domain of (f/g)(x) is -3 < x ≤ ∞. So, any numbers greater than -3 and less than or equal to infinity, are possible solutions to this function. Therefore, -2, 3, 7, and many more numbers greater than -3 are possible solutions.

Answer 2

Answer: A. Part A:

f(4) = 9x + 27 = 9(4) + 27 = 36 + 27 = 63

g(4) = x + 3 = 4 + 3 = 7

B. Part B:

f(x) / g(x) = (9x + 27) / (x + 3) = 9

f(4) / g(4) = 63 / 7 = 9

C. Part C:

The domain of f(x) / g(x) is all real numbers except x = -3, because dividing by zero is undefined. The domain of f(x) / g(x) is all real numbers except x = -3.

Explanation: