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The function f(x) =3/4 ⋅ 10⁻ˣ is reflected across the x-axis to create the function g(x). Which ordered pair is on g(x)?

1. (-3,-3/1000)
2. (-2, 75)
3. (2, -3/400)
4. (3, -750)

1 Answer

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Final answer:

The function f(x) = 3/4 ⋅ 10^-x is reflected across the x-axis to create the function g(x). To determine which ordered pair is on g(x), we need to reflect the y-coordinate of the given options and substitute the x-values into the reflected function.

Step-by-step explanation:

The function f(x) = 3/4 ⋅ 10-x is reflected across the x-axis to create the function g(x). To find which ordered pair is on g(x), we need to reflect the given ordered pairs across the x-axis. Let's take option 1 as an example.

Option 1: (-3, -3/1000)

To reflect the y-coordinate, we change the sign, so (-3, -3/1000) becomes (-3, 3/1000). Now, we substitute x = -3 into g(x) and check if g(-3) = 3/1000. Plugging in the value, we get: g(-3) = 3/4 ⋅ 103 = 3000/4 = 750 which is not equal to 3/1000. Therefore, (-3, 3/1000) is not on g(x). Now, you can go through the remaining options and check which one satisfies g(x).

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