Problem

Analyze \(f(x)~=~2^{x~-~3}\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay and the translation; give the intercepts, asymptote, domain, range, and monotonic behavior; and compute exact anchors at \(x~=~2\), \(3\), and \(4\).

Prompt coordinate grid scaled for the stated exponential equation; the curve, anchors, and asymptote are withheld.

Answer choices

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Parameters: a = 1, b = 2, h = 3, k = 0.
Class: growth because b > 1; shift right 3.
Features: y-intercept (0, 1); asymptote y = 0; domain all real numbers; range y > 0; increasing.
Anchors: (2, 1/2), (3, 1), (4, 2).

Parameters: a = 1, b = 2, h = 3, k = 0.
Class: growth because b > 1; shift right 3.
Features: y-intercept (0, 1/8); asymptote x = 0; domain x > 0; range all real numbers; increasing.
Anchors: (2, 1/2), (3, 1), (4, 2).

Parameters: a = 1, b = 2, h = −3, k = 0.
Class: growth because b > 1; shift left 3.
Features: y-intercept (0, 8); asymptote y = 0; domain all real numbers; range y > 0; increasing.
Anchors: (−4, 1/2), (−3, 1), (−2, 2).

Parameters: a = 1, b = 2, h = 3, k = 0.
Class: growth because b > 1; shift right 3.
Features: y-intercept (0, 1/8); asymptote y = 0; domain all real numbers; range y > 0; increasing.
Anchors: (2, 1/2), (3, 1), (4, 2).

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Analyze \(f(x)~=~2^{x~-~3}\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay and the translation; give the intercepts, asymptote, domain, range, and monotonic behavior; and compute exact anchors at \(x~=~2\), \(3\), and \(4\).

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