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Nonlinear functions SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

The function $f$ is defined by $f (x) = 270 (0.1)^{x}$ . What is the value of $f (0)$ ?

ExplanationShow

Choice D is correct. The value of $f (0)$ is the value of $f (x)$ when $x = 0$ . Substituting $0$ for $x$ in the given function yields $f (0) = 270 (0.1)^{0}$ , or $f (0) = 270 (1)$ , which is equivalent to $f (0) = 270$ . Therefore, the value of $f (0)$ is $270$ .

Choice A is incorrect. This is the value of $x$ , not $f (x)$ .

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

Choice C is incorrect. This is the value of $f (1)$ , not $f (0)$ .

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