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Find g(x), where g(x) is the reflection across the y-axis of f(x)=–2x–8.g(x)=2x+8g(x)=2x–8g(x)=–2x–8g(x)=–2x+8Submit

Question

Find g(x), where g(x) is the reflection across the y-axis of f(x)=–2x–8.

  • g(x) = 2x + 8
  • g(x) = 2x – 8
  • g(x) = –2x – 8
  • g(x) = –2x + 8

Submit

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Solution

To find g(x) g(x) , the reflection across the y-axis of the function f(x)=2x8 f(x) = -2x - 8 , we can follow these steps:

1. Break Down the Problem

We need to find the reflection of the given function f(x) f(x) across the y-axis. For a function f(x) f(x) , its reflection across the y-axis is g(x)=f(x) g(x) = f(-x) .

2. Relevant Concepts

The reflection across the y-axis involves replacing x x with x -x in the original function. Therefore, if f(x)=2x8 f(x) = -2x - 8 , then:

g(x)=f(x) g(x) = f(-x)

3. Analysis and Detail

Now we will replace x x in the equation f(x) f(x) with x -x :

g(x)=f(x)=2(x)8 g(x) = f(-x) = -2(-x) - 8 g(x)=2x8 g(x) = 2x - 8

4. Verify and Summarize

Having calculated g(x) g(x) , we can summarize:

  • The original function is f(x)=2x8 f(x) = -2x - 8 .
  • The reflection across the y-axis gives us g(x)=2x8 g(x) = 2x - 8 .

Final Answer

Therefore, the reflection g(x) g(x) is: g(x)=2x8 g(x) = 2x - 8

This problem has been solved

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