The function f(x) = x2. The graph of g(x) is f(x) translated to the right 3 units and down 3 units. What is the function rule fo

Question

3 years ago

11

r g(x)?

1 answer:

Kaylis [27] · Answer 1 · 2022-01-07T12:41:20+03:00

The rule for g(x) is: $f(x) = (x-3)^2-3$

Step-by-step explanation:

Given function is:

$f(x) = x^2$

When a function f(x) is shifted right or left, b units the new function is written as:

$f(x) = x$

Shifting right

$g(x) = f(x-b)$

Shifting left

$g(x) = f(x+b)$

Similarly, when shifting up or down

$g(x) = f(x)+b => Up\\g(x) = f(x) - b => Down$

As our given function is shifted 3 units to the right, it will be written as:

$f(x) = (x-3)^2$

The function is when moved down 3 units, then

$f(x) = (x-3)^2-3$

Hence

The rule for g(x) is: $f(x) = (x-3)^2-3$

Keywords: Function transformation, Functions

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