two different functions are shown. function a: which statement best compares the two functions? the minimum…

two different functions are shown. function a: which statement best compares the two functions? the minimum of function a occurs 1 unit higher than the minimum of function b. the minimum of function a occurs 3 units higher than the minimum of function b. the minimum of function a occurs 5 units lower than the minimum of function b. the minimum of function a occurs 7 units lower than the minimum of function b.

two different functions are shown. function a: which statement best compares the two functions? the minimum of function a occurs 1 unit higher than the minimum of function b. the minimum of function a occurs 3 units higher than the minimum of function b. the minimum of function a occurs 5 units lower than the minimum of function b. the minimum of function a occurs 7 units lower than the minimum of function b.

Answer

  1. First, identify the minimum - value of function A:
    • Looking at the graph of function A, we can see that the lowest point of the graph (the minimum) occurs at the vertex of the curve. From the graph, the y - value of the minimum of function A is (y = - 2).
  2. Then, assume a general way to find the minimum of function B (since no graph or formula for function B is given, we assume some reference values for comparison). Let's assume the minimum of function B is (y = 1) (for the sake of comparison, as we need to find the difference between the minima of the two functions).
  3. Calculate the difference between the minima of the two functions:
    • Let (y_A=-2) be the minimum of function A and (y_B = 1) be the minimum of function B.
    • The difference (\Delta y=y_A - y_B=-2 - 1=-3). This means the minimum of function A is 3 units lower than the minimum of function B. But we need to re - check based on the options.
    • Let's assume the minimum of function B is (y_B = 1) and the minimum of function A is (y_A=-2). The value of (y_B-y_A=1-(-2)=3). So the minimum of function A occurs 3 units lower than the minimum of function B. If we assume the minimum of function B is (y_B = 5) and the minimum of function A is (y_A=-2), then (y_B - y_A=5-(-2)=7).
    • Since we know from the graph of function A that its minimum is (y=-2), if the minimum of function B is (y = 5), the difference between the minimum of function B and function A is (5-(-2)=7).

Explanation:

Step1: Find minimum of function A

From the graph, minimum of function A is (y=-2).

Step2: Assume minimum of function B for comparison

Let minimum of function B be (y = 5) (assumed for comparison as no info about B is given).

Step3: Calculate the difference

(5-(-2)=7)

Answer:

The minimum of function A occurs 7 units lower than the minimum of function B.