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On a coordinate plane, 2 curves are shown. The first curve f (x) opens up and to the right in quadrant 1. It goes through (4, 2), (1, 4), and crosses the y-axis at (0, 5). The second curve g (x) opens down and to the right and goes through (4, negative 2), (1, negative 4), and crosses the y-axis at (0, negative 5). Which function represents a reflection of f(x) = 5(0.8)x across the x-axis? g(x) = 5(0.8)–x g(x) = –5(0.8)x g(x) = One-fifth(0.8)x g(x) = 5(–0.8)x

Answer :

Answer:

g(x) = –5*(0.8)^x

Step-by-step explanation:

In order to get the reflection of a function across the x-axis, you have to multiply that function by (-1)

Given the function:

f(x) = 5*(0.8)^x

then, its reflection across the x-axis is -f(x) = g(x) = –5*(0.8)^x. This result can be checked replacing the known points into the equation, as follows:

x |  g(x)

0 | –5*(0.8)^0 = -5

1  | –5*(0.8)^1 = -4

4 | –5*(0.8)^4 = -2

jayilych4real

The function that represents a reflection of f(x) = 5(0.8)x across the x-axis is B. g(x) = –5*(0.8)^x

Calculations and Parameters:

To get the reflection of a function across the x-axis, you have to multiply that function by (-1)

The function is:

f(x) = 5*(0.8)^x

Hence, to find the reflection across the x-axis is:

-f(x) = g(x) = –5*(0.8)^x.

This can be validated by checking it:

  • x |  g(x)
  • 0 | –5*(0.8)^0 = -5
  • 1  | –5*(0.8)^1 = -4
  • 4 | –5*(0.8)^4 = -2

Therefore, the correct answer is option B.

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