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Mazyrski [523]
3 years ago
14

Given the function f(x)=g(x-3)+2, describe transformation of f(x) on a coordinate plane relative to g(x).

Mathematics
1 answer:
Fantom [35]3 years ago
3 0
<h2>Answer:</h2>

The transformation of f(x) on a coordinate plane relative to g(x) is that the graph of g(x) has been shifted three units to the right and two units upward.

<h2>Step-by-step explanation:</h2>

If \ c \ is \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=g(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ f(x)=g(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ f(x)=g(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ f(x)=g(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ f(x)=g(x+c)

By knowing this, we can see that the function f(x) takes the following form:

f(x)=g(x-c)+k

Therefore, we can say that g(x-3) represents shifting the graph three units to the right and ultimately g(x-3)+2 tells us that the graph is shifted two units upward. Finally:

  • The transformation of f(x) on a coordinate plane relative to g(x) is that the graph of g(x) has been shifted three units to the right and two units upward.
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