Problem

Analyze \(f(x)~=~4~\cdot~3^x~-~2\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay; give the intercepts, asymptote, domain, range, and monotonic behavior; and compute exact anchors at \(x~=~-1\), \(0\), and \(1\).

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

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Parameters: a = 4, b = 3, h = 0, k = −2.
Class: growth because b > 1.
Features: y-intercept (0, 2); asymptote y = −2; domain all real numbers; range y > −2; increasing.
Anchors: (−1, −2/3), (0, 2), (1, 10).

Parameters: a = −4, b = 3, h = 0, k = −2.
Class: growth base reflected across the x-axis.
Features: y-intercept (0, −6); asymptote y = −2; domain all real numbers; range y < −2; decreasing.
Anchors: (−1, −10/3), (0, −6), (1, −14).

Parameters: a = 4, b = 3, h = 0, k = 2.
Class: growth because b > 1.
Features: y-intercept (0, 6); asymptote y = 2; domain all real numbers; range y > 2; increasing.
Anchors: (−1, 10/3), (0, 6), (1, 14).

Parameters: a = 4, b = 3, h = 0, k = −2.
Class: growth because b > 1.
Features: y-intercept (0, 4); asymptote y = −2; domain all real numbers; range y > −2; increasing.
Anchors: (−1, −2/3), (0, 4), (1, 10).

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Analyze \(f(x)~=~4~\cdot~3^x~-~2\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay; give the intercepts, asymptote, domain, range, and monotonic behavior; and compute exact anchors at \(x~=~-1\), \(0\), and \(1\).

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