Problem

Analyze \(f(x)~=~-4(0.75)^x\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay and any reflection; give the intercepts, asymptote, domain, range, and monotonic behavior; and compute exact anchors at \(x~=~-1,~0,~\text{and}~1\).

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

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Parameters: a = −4, b = 0.75, h = 0, k = 0.
Class: decay because 0 < b < 1; reflected across the x-axis.
Features: y-intercept (0, −4); asymptote y = 0; domain all real numbers; range y < 0; decreasing.
Anchors: (−1, −16/3), (0, −4), (1, −3).

Parameters: a = −4, b = 0.75, h = 0, k = 0.
Class: decay because 0 < b < 1; reflected across the x-axis.
Features: y-intercept (0, −4); asymptote y = 0; domain all real numbers; range y < 0; increasing.
Anchors: (−1, −16/3), (0, −4), (1, −3).

Parameters: a = 4, b = 0.75, h = 0, k = 0.
Class: decay because 0 < b < 1; no x-axis reflection.
Features: y-intercept (0, 4); asymptote y = 0; domain all real numbers; range y > 0; decreasing.
Anchors: (−1, 16/3), (0, 4), (1, 3).

Parameters: a = −4, b = 0.75, h = 0, k = 0.
Class: growth because b > 1; reflected across the x-axis.
Features: y-intercept (0, −4); asymptote y = 0; domain all real numbers; range y < 0; increasing.
Anchors: (−1, −16/3), (0, −4), (1, −3).

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Analyze \(f(x)~=~-4(0.75)^x\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay and any reflection; give the intercepts, asymptote, domain, range, and monotonic behavior; and compute exact anchors at \(x~=~-1,~0,~\text{and}~1\).

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