Problem

Analyze \(f(x)~=~5(1.2)^x~+~4\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay; give the intercepts, asymptote, domain, range, and monotonic behavior; compute the anchors at \(x~=~0\) and \(1\); and map the parent anchor \((0,~1)\).

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

Answer choices

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Parameters: a = 5, b = 1.2, h = 0, k = 4.
Class: growth because b > 1.
Features: y-intercept (0, 5); asymptote y = 4; domain all real numbers; range y > 4; increasing.
Anchors: (0, 5), (1, 10); parent anchor (0, 1) maps to (0, 5).

Parameters: a = −5, b = 1.2, h = 0, k = 4.
Class: growth base reflected across the x-axis.
Features: y-intercept (0, −1); asymptote y = 4; domain all real numbers; range y < 4; decreasing.
Anchors: (0, −1), (1, −2); parent anchor (0, 1) maps to (0, −1).

Parameters: a = 5, b = 1.2, h = 0, k = 5.
Class: growth because b > 1.
Features: y-intercept (0, 10); asymptote y = 5; domain all real numbers; range y > 5; increasing.
Anchors: (0, 10), (1, 11); parent anchor (0, 1) maps to (0, 10).

Parameters: a = 5, b = 1.2, h = 0, k = 4.
Class: growth because b > 1.
Features: y-intercept (0, 9); asymptote y = 4; domain all real numbers; range y > 4; increasing.
Anchors: (0, 9), (1, 10); parent anchor (0, 1) maps to (0, 9).

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Analyze \(f(x)~=~5(1.2)^x~+~4\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay; give the intercepts, asymptote, domain, range, and monotonic behavior; compute the anchors at \(x~=~0\) and \(1\); and map the parent anchor \((0,~1)\).

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