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yKpoI14uk [10]
3 years ago
12

Describe each graph in relation to its basic function.

Mathematics
1 answer:
emmainna [20.7K]3 years ago
8 0

Answer:

In a nutshell, f(x) is obtained by applying an horizontal translation on g(x), followed by a vertical translation.

Step-by-step explanation:

Let be g(x) = x^{3} the parent function, f(x) is obtained by applying an horizontal translation on g(x), followed by a vertical translation, that is:

f(x) = g(x-a)-b,\,a,b\in\mathbb{R} (1)

If a > 0, then translation is rightwards.

If b > 0, then translation in downwars.

If a = 2 and b = 1, then the resulting function is:

f(x) = g(x-2)-1

f(x) = (x-2)^{3}-1 (2)

In a nutshell, f(x) is obtained by applying an horizontal translation on g(x), followed by a vertical translation.

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