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Advanced Math / Nonlinear functions Difficulty: Hard

The function $f$ is defined by $f (x) = (- 8) {(2)}^{x} + 22$ . What is the y-intercept of the graph of $y = f (x)$ in the xy-plane?

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Explanation

Choice A is correct. The y-intercept of the graph of $y = f (x)$ in the xy-plane occurs at the point on the graph where $x equals 0$ . In other words, when $x equals 0$ , the corresponding value of $f (x)$ is the y-coordinate of the y-intercept. Substituting $0$ for $x$ in the given equation yields $f (0) = (- 8) {(2)}^{0} + 22$ , which is equivalent to $f (0) = (- 8) (1) + 22$ , or $f left parenthesis 0 right parenthesis equals 14$ . Thus, when $x equals 0$ , the corresponding value of $f (x)$ is $14$ . Therefore, the y-intercept of the graph of $y = f (x)$ in the xy-plane is $left parenthesis 0 comma 14 right parenthesis$ .

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

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

Choice D is incorrect. This could be the y-intercept for $f (x) = (- 8) {(2)}^{x}$ , not $f (x) = (- 8) {(2)}^{x} + 22$ .