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Advanced Math / Nonlinear functions Difficulty: Medium

The graph of the rational function $f$ is shown, where $y = f (x)$ and $x greater than or equals 0$ . Which of the following is the graph of $y = f (x) + 5$ , where $x greater than or equals 0$ ?

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Explanation

Choice D is correct. It's given that the graph of the rational function $f$ is shown, where $y = f (x)$ and $x greater than or equals 0$ . The graph shown passes through the point $left parenthesis 3 comma 3 right parenthesis$ . It follows that when the value of $x$ is $3$ , the value of $f (x)$ is $3$ . When the value of $f (x)$ is $3$ , the value of $f left parenthesis x right parenthesis plus 5$ is $3 plus 5$ , or $8$ . Therefore, the graph of $y = f (x) + 5$ passes through the point $left parenthesis 3 comma 8 right parenthesis$ . Of the given choices, choice D is the only graph that passes through the point $left parenthesis 3 comma 8 right parenthesis$ and is therefore the graph of $y = f (x) + 5$ .

Choice A is incorrect. This is the graph of $y = f (x) - 5$ , rather than $y = f (x) + 5$ .

Choice B is incorrect. This is the graph of $y = \frac{f (x)}{5}$ , rather than $y = f (x) + 5$ .

Choice C is incorrect and may result from conceptual or calculation errors.