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Advanced Math Difficulty: Medium

$f (x) = x^{5} + 9 x + 17$

For the given function $f$ , the graph of $y = f (x)$ in the xy-plane passes through the point $left parenthesis 0 comma b right parenthesis$ , where $b$ is a constant. What is the value of $b$ ?

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Explanation

The correct answer is $17$ . It's given that the graph of $y = f (x)$ in the xy-plane passes through the point $left parenthesis 0 comma b right parenthesis$ , where $b$ is a constant. It follows that $f left parenthesis 0 right parenthesis$ equals $b$ . Substituting $0$ for $x$ in the given function yields $f (0) = 0^{5} + 9 (0) + 17$ , or $f left parenthesis 0 right parenthesis equals 17$ . Therefore, the value of $b$ is $17$ .