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f(x) Transforms to f(x+a) or f(x-a)

If the graph ...

Question

If the graph $y = g (x)$ has a minimum point at $(1, 2),$ then minimum point of the graph $y = g (x - 3) - 4$ is

(- 2, 6)

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(- 3, 5)

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(4, - 2)

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(1, 2)

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Solution

The correct option is C $(4, - 2)$
The minimum point of $y = g (x)$ is $(1, 2)$
Shifting $y = g (x)$ vertically downward by $4$ units, we get
$y = g (x) - 4$
Now, the minimum point shifts to $(1, 2 - 4) = (1, - 2)$
Shifting $y = g (x) - 4$ by $3$ units to right, we get
$y = g (x - 3) - 4$
Now, the minimum point shifts to $(1 + 3, - 2) = (4, - 2)$

Hence, the required minimum point is $(4, - 2)$

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f(x) Transforms to f(x+a) or f(x-a)

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If the graph y=g(x) has a minimum point at (1,2), then minimum point of the graph y=g(x−3)−4 is

If the graph $y = g (x)$ has a minimum point at $(1, 2),$ then minimum point of the graph $y = g (x - 3) - 4$ is