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Identify the horizontal asymptote, initial value, domain, and range of the function.

Identify the horizontal asymptote, initial value, domain, and range of the function-example-1

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The key features of the graph of this function include;

horizontal asymptote: y = 4.

initial value: 3.

domain: (-∞, ∞)

range: (-∞, 4).

In Mathematics and Euclidean Geometry, a horizontal asymptote is a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

A range is the set of all real numbers that connects with the elements of a domain for any function, usually read from bottom to top.

A domain is the set of all real numbers (x-values) for which a particular relation or function is defined.

By critically observing the graph of this exponential function, we can logically deduce the following key features;

Horizontal asymptote: y = 4.

The y-intercept or initial value: 3.

domain: (-∞, ∞) or x ∈ R

range: (-∞, 4) or y

User Chris Arndt
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