Question #45df91ee - SAT Suite Question Bank

ID: 45df91ee

Modded SAT Question Bank by Abdullah Mallik

$g left parenthesis x right parenthesis equals 11 left parenthesis one twelfth right parenthesis Superscript x$

If the given function $g$ is graphed in the xy-plane, where $y = g (x)$ , what is the y-intercept of the graph?

$left parenthesis 0 comma 11 right parenthesis$
$left parenthesis 0 comma 132 right parenthesis$
$left parenthesis 0 comma 1 right parenthesis$
$left parenthesis 0 comma 12 right parenthesis$

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Correct Answer: A

Rationale

Choice A is correct. The x-coordinate of any y-intercept of a graph is $0$ . Substituting $0$ for $x$ in the given equation yields $g left parenthesis 0 right parenthesis equals 11 left parenthesis one twelfth right parenthesis Superscript 0$ . Since any nonzero number raised to the $0 th$ power is $1$ , this gives $g left parenthesis 0 right parenthesis equals 11 dot 1$ , or $g left parenthesis 0 right parenthesis equals 11$ . The y-intercept of the graph is, therefore, the point $left parenthesis 0 comma 11 right parenthesis$ .

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 and may result from conceptual or calculation errors.

Question Difficulty: Medium