The rule for g(x) is: [tex]f(x) = (x-3)^2-3[/tex]
Step-by-step explanation:
Given function is:
[tex]f(x) = x^2[/tex]
When a function f(x) is shifted right or left, b units the new function is written as:
[tex]f(x) = x[/tex]
Shifting right
[tex]g(x) = f(x-b)[/tex]
Shifting left
[tex]g(x) = f(x+b)[/tex]
Similarly, when shifting up or down
[tex]g(x) = f(x)+b => Up\\g(x) = f(x) - b => Down[/tex]
As our given function is shifted 3 units to the right, it will be written as:
[tex]f(x) = (x-3)^2[/tex]
The function is when moved down 3 units, then
[tex]f(x) = (x-3)^2-3[/tex]
Hence
The rule for g(x) is: [tex]f(x) = (x-3)^2-3[/tex]
Keywords: Function transformation, Functions
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