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Advanced Math / Nonlinear functions Difficulty: Easy

The graph shown will be translated up $4$ units. Which of the following will be the resulting graph?

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Explanation

Choice A is correct. When a graph is translated up $4$ units, each point on the resulting graph is $4$ units above the point on the original graph. In other words, the y-value of each point on the graph increases by $4$ . The graph shown passes through the points $left parenthesis 1 comma negative 1 right parenthesis$ , $left parenthesis 2 comma negative 2 right parenthesis$ , and $left parenthesis 3 comma negative 1 right parenthesis$ . It follows that when the graph shown is translated up $4$ units, the resulting graph will pass through the points $(1, - 1 + 4)$ , $(2, - 2 + 4)$ , and $(3, - 1 + 4)$ . These points are $left parenthesis 1 comma 3 right parenthesis$ , $left parenthesis 2 comma 2 right parenthesis$ , and $left parenthesis 3 comma 3 right parenthesis$ , respectively. Of the given choices, only the graph in choice A passes through the points $left parenthesis 1 comma 3 right parenthesis$ , $left parenthesis 2 comma 2 right parenthesis$ , and $left parenthesis 3 comma 3 right parenthesis$ .

Choice B is incorrect. This is the result of translating the graph down, rather than up, $4$ units.

Choice C is incorrect. This is the result of translating the graph left, rather than up, $4$ units.

Choice D is incorrect. This is the result of translating the graph right, rather than up, $4$ units.