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For an unknown parent function f(x), write a function g(x) that is:-vertically stretched by a factor of 2,- shifted up 5 units, and - shifted right 4 units. Explain how your function accomplishes these transformations.

Respuesta :

Given the parent function to be:

[tex]f(x)[/tex]

Write the function g(x), when the parent function is

1. vertically stretched by a factor of 2 - Multiply the parent function by 2

[tex]g(x)=2f(x)[/tex]

2. Shifted up 5 units - Add 5 units outside of the parent function

[tex]g(x)=2f(x)+5[/tex]

3. Shifted right 4 units - Subtract 4 from within the parent function

[tex]g(x)=2f(x-4)+5[/tex]

Therefore, the transformation of the parent function f(x) to g(x) is

[tex]g(x)=2f(x-4)+5[/tex]

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